Jika saat SD dan SMP kalian sudah dikenalkan dengan lingkaran, maka di SMA kalian akan mempelajari lingkaran lagi. Tapi, di SMA materinya persamaan lingkaran, yuk cek contoh soal dan pembahasannya:
Kalian bisa pelajari soal ini di chanel youtube ajar hitung, kalian bisa langsung klik video link di bawah ini:
Kalian bisa pelajari soal ini di chanel youtube ajar hitung, kalian bisa langsung klik video link di bawah ini:
1. Persamaan lingkaran berpusat di titik (2, 3) dan melalui titik (5, -1) adalah...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhplKdkkB-xqdi7tnXOq_PwlW4Yp4_SvAVQwlhxBr9iM1BZiNXlCM-SPB1xDC0mEJ9roNygAbM_JrlY70R5GHDQtzb7X-0rf40NI2LR6FDP3qj14r6iJHghb1mt5EshgvF-L2WHqrNcuhw/s1600/a.png)
Persamaan lingkaran yang berpusat di (2, 3) dan melalui titik (5, -1)adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9f1fHBP4Phbp2aqNtC-nLdyZ089I4Pf90mb8c5B7MzVjaPyfGBD03Y7jUFz0dvwwdJQ9glzvJM4IInucavmtOh7mpTFsJOMa8m2zIpbdGCglJaGwKvzDHQk8CSdw2sHpbHDcYPSvdyWk/s1600/a.png)
r = √25
r = 5
sehingga persamaan lingkarannya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG9ONtZ1KXaEldWqqGE_izkZ457VZ3UJiTsjYgI2XeKred0tOG6gatM5-w6YTtn6tqroG8_3oGn6z6bY_g7VOIgId7jHDUF5LAPDh9f4ZiPFAseo5yRwH5qbm6WtAD_wyyuBIQU8QLwLg/s1600/a.png)
jawaban: A
2. Persamaan garis singgung lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg970-DJxL-J2q67dl7vlRAmVyqFrkWbmVeb4Q6LSduqHHsBuA8ElSRRetv4Y3Y7gauaoq-mVI0nPzj0DfNz-35HFBnO8GKKaHY6IDzRIiSK1aBXXKkOhG0CJO9Zv052_GJD07zUyoLqfk/s1600/a.png)
a. 3x – 4y – 41 = 0
b. 4x + 3y – 55 = 0
c. 4x – 5y – 53 = 0
d. 4x + 3y – 31 = 0
e. 4x – 3y – 40 = 0
Pembahasan:
Persamaan garis singgung lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg970-DJxL-J2q67dl7vlRAmVyqFrkWbmVeb4Q6LSduqHHsBuA8ElSRRetv4Y3Y7gauaoq-mVI0nPzj0DfNz-35HFBnO8GKKaHY6IDzRIiSK1aBXXKkOhG0CJO9Zv052_GJD07zUyoLqfk/s1600/a.png)
x1.x + y1.y + a(x1 + x) + b (y1 + y) + c = 0
x1.x + y1.y – ½ . 6 (x1 + x) + ½ . 4 (y1 + y) - 12 = 0
7.x + 1.y – 3 (7 + x) + 2 (1 + y) - 12 = 0
7x + y – 21 – 3x + 2 + 2y – 12 = 0
4x + 3y – 31 = 0
Jawaban: D
3. Lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguvFnxsL_58mzQo65KDJRVtq8iqB8EtU-a39_yYhFocpt1QESk1wMPtgWQFEOi68CsQ_e4vlfPF5NOI6zVMXy-VF3QE95gTnJnd6RIFZ1yiprONVDgkLwM0FSXjv-ryFDEOm8Flipx6lg/s1600/a.png)
a. x = 2 dan x = 4
b. x = 3 dan x = 1
c. x = 1 dan x = 5
d. x = 2 dan x = 3
e. x = 3 dan x = 4
pembahasan:
Lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguvFnxsL_58mzQo65KDJRVtq8iqB8EtU-a39_yYhFocpt1QESk1wMPtgWQFEOi68CsQ_e4vlfPF5NOI6zVMXy-VF3QE95gTnJnd6RIFZ1yiprONVDgkLwM0FSXjv-ryFDEOm8Flipx6lg/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJ_WSCjfs5iL9nzgbWB1RQblCigV4rpSDgKm-fJtbe6wsexNHUaVgkljV0E3SGJRIN_tcCbKRLsfqsFAs9Rgaz8iSIyKCALmyTpHYuZPyTHZg0-49gVGnX4au3O0gR928y6-1oZQbXWIM/s1600/a.png)
x = 2 dan x = 4
jadi, titik potongnya (2, 1) dan (4, 1)
persamaan lingkarannya menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8kjGMMSCPhL8AfsWTvlwqr_8VXA5p1YYq2zEo1PM4tll1zAbT_H44nHaxHH6XFL9nuTYmNFe6dmSCfvzU4VUBlRC3wE4PExJZ9gA2Kb-RuotUzwmrh1ljMEh-SKbAP97vHiTlYJ_20CQ/s1600/a.png)
persamaan garis singgung terhadap lingkaran L melalui titik (2, 1) adalah:
x1.x + y1.y + a(x1 + x) + b (y1 + y) + c = 0
x1.x + y1.y – ½ . 6 (x1 + x) - ½ . 2 (y1 + y) + 9 = 0
2.x + 1.y – 3 (2 + x) - 1 (1 + y) + 9 = 0
2x + y – 6 – 3x – 1 – y + 9 = 0
-x + 2 = 0
x = 2
persamaan garis singgung terhadap lingkaran L melalui titik (4, 1) adalah:
x1.x + y1.y + a(x1 + x) + b (y1 + y) + c = 0
x1.x + y1.y – ½ . 6 (x1 + x) - ½ . 2 (y1 + y) + 9 = 0
4.x + 1.y – 3 (4 + x) - 1 (1 + y) + 9 = 0
4x + y – 12 – 3x – 1 – y + 9 = 0
x - 4 = 0
x = 4
jawaban: A
4. persamaan lingkaran dengan pusat (3 , -2) dan menyinggung sumbu Y adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzwXTr_wgJbdSez9uG6ZHRixarju5x0HHVsnMBVRNyU7O2dPoxMp5DwIGTmP3zstHVTaAoLUF4KwPHkrpecvw1ttrQZpUvpb_sfk3NCfHD71jE1UmcxUw5BXQ7SA_sTpGdou8MZqupfjk/s1600/a.png)
Pembahasan:
Rumus persamaan lingkaran dengan pusat (a, b) adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZRCnu98IArMzdB-fsmX50TX3-JqdqvbkWoJnxvB7USXNQm00s0a9KKybSdIkr1_ppGunktgs6Bc7VVYK7ayuSW2AElcKTjD_IZiwrDMovle366ioloG95wHatBG1WASKffJiCt8SKypY/s1600/a.png)
Karena, garis menyinggung sumbu y, maka jari-jari = x = 3 (karena pusatnya (3, -2), sehingga:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgrWRclZaE73Qs7c3tnHJqCZvFZ1BIeBgUNRjuhZTJyMOFJH9pbdusondqeaIGLqTqrHN4qxEpOxopN0EER6_wtsT2eR-PzxGW2VWjh1oJzu6oNnZ13Doi1dRo8VWz6_XVXdbGL4Hi-Rw/s1600/a.png)
jawaban: D
5. Jarak antara titik pusat lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8PYRBByponWp0n5mmhxs1szmVpjiBJ4faR-Lhxo6RCdXDjBiZYzCesx52yEWB03rm5uhi0fLdlRxIj-Bf-tYMy4oLVOJXJTBBH1-HoG6nQTmqx-sJfFMGDG_VB0MEQk-hNl07d-CcXPM/s1600/a.png)
a. 3
b. 2,5
c. 2
d. 1,5
e. 1
Pembahasan:
Lingkaran dengan persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxBdn1LDz2L1NKj7sR4R1YgSHDk2zqS0eRkaduB-Smjb7OZGlmTdr4VNJzgsMPmkp7QuV5_KwegARcnsO3u4WxGyfYrQRaEnEyDZJRaiKCj0vOWXIkY8cnh0M7LW_nqBEDf2aqDYWhWKA/s1600/a.png)
( - ½ .(-4) , - ½ . (0)) = (2, 0)
Karena, titik pusatnya (2, 0) maka jarak lingkaran ke sumbu y = x = 2
Jawaban: C
6. Lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXP7vlB-rN9teorsB8Tb4Rf93b8JIhfxcPtoq2pnbGiiAfkPgtBeEvtNd6_ehKtbx-Hikp7cEuUHYh985z_uyg9IcPzCxx9on_KC0fT6pMK3g7x10_p8PBxH28Ak771bf6nkOZurWZo0k/s1600/a.png)
a. (4, 6)
b. (4, -6)
c. (4, 4)
d. (4, 1)
e. (4, -1)
Pembahasan:
Lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXP7vlB-rN9teorsB8Tb4Rf93b8JIhfxcPtoq2pnbGiiAfkPgtBeEvtNd6_ehKtbx-Hikp7cEuUHYh985z_uyg9IcPzCxx9on_KC0fT6pMK3g7x10_p8PBxH28Ak771bf6nkOZurWZo0k/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCjMdZQcVPNc6hYkMl-mqCXiKs1KavNc_WsbEkVjC_cJNNTeC8GQdXl6huPtxGFNv6jpcehBixO5aalk1qFPxEQ8_HhY-pxZ6YeF7c1ARs-kJqkglmLU5S3jsDttaRDnCBFXQCm1UM6oI/s1600/a.png)
(y + 1) (y + 1) = 0
y = -1
jadi, lingkaran menyinggung di titik ( 4, -1)
jawaban: E
7. Lingkaran yang sepusat dengan lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuhJ2PDkrIcQoEI1EvcaPSQ-egCpykRfV5_dEKrkCr-S9fXhB2XoTJ5LBkZTgqP8CbwxEsylhj2SS0aOeWCSwXR8Y0CCY8iR4-jMMD1FG7klE2IzdGwXmBtv-KNbekHiMFedvxsoSm1FM/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJS4ZNjIUJGACjrCIJkukvnCWbBHCMkDEkauh_1d9gdrlQCx1Ewd8aJ-cdQAaXtlg1m476DHRIfi4pNB343hc3iftY5_8esCLD-wFJQ87cMNf5C4a9tZc_92nbZwm8opOG9C6IfFItF9Y/s1600/a.png)
Pembahasan:
Lingkaran dengan persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxBdn1LDz2L1NKj7sR4R1YgSHDk2zqS0eRkaduB-Smjb7OZGlmTdr4VNJzgsMPmkp7QuV5_KwegARcnsO3u4WxGyfYrQRaEnEyDZJRaiKCj0vOWXIkY8cnh0M7LW_nqBEDf2aqDYWhWKA/s1600/a.png)
( - ½ . (-4), - ½ . 6) = ( 2, -3)
Sehingga persamaan garis yang berpusat di (2, -3) adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNxaoqvRGdm0yQ1jzA9roo_aUwKcRiTxr1m6-Aw3cQ4FLD5a3eLbszlQMZVlpScpV8Q-m8iVsF74AUr3dC8Q-bv5zUQfEmIlLkkNsdbFZba5M3_CZuopyOl7iVi05UyvDU6FbVKY_QkrA/s1600/a.png)
Panjang jari-jari (r) lingkaran adalah jarak titik pusat (2, -3) ke garis 3x – 4y + 7 = 0, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz-yLhiYAUEbXHo6ClgEoxZYgpbUql9CBMsY7Xxbd6GHCW5svIqBo4bhoyogLdqkxpgf9HNgMnpCP-YmTuMAS2GZ5wG3nljx5298bapZZL1fJP518hqhyLUf4KQxMVaVU45zK_9oQCqkI/s1600/a.png)
jadi, persamaan lingkarannya menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZutzxeMwAyeMmuZoxukMZEbn11AFPQREQgvb6n5whScxq7kYVM8Zroui2LsEqyl_x2Jah1jdPDo0pEclXDYed7qZXROBEswgTi6w08aWZk_isH-0qaaBIMkCnFyqkIzjz1aqnn1nvPmA/s1600/a.png)
Jawaban: A
8. Diketahui lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrivBNPtr2ZvvDdG0PKfxkNOZ2DGfdMzoQ-tMYSBZgpeWd2HvP5D1yqNEcGHPoAR-pZtR3C5tDqtfw_W92_BBcp2u1oJxigUpwu1aTGuaRFPMjefCs-Lq2Vkph4dpEs0vcSMoaO2KcyRM/s1600/a.png)
a. (-5, -3)
b. (-5, 3)
c. (6, -5)
d. (-6, -5)
e. (3, -5)
Pembahasan:
Rumus jari-jari adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQZs0iRtJzOoWjyftggJ3dobFXZd6CJ3btnyqSORZ_LiKqyxIlJ4EFzevzenJN4MfkxwU4-H0FSj1m0nV5lHZf0_3uY2J7sv1JehwnWDlnPgGj4hdoxCHcZmEg-7mZvsAdzw69Hdbr3vA/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVvPUesIXSysPTftpvk2VP8HUewZAAl0k3H1OhtHR7IkjiC0V60ED6eaGvBvYF1YVdmXXToPXVWe2hyphenhyphenFVwZ9eYFfoTpRuZYH8V53p01LXlpKiOz0uWBdTRgSsNqGThPDnZAMJ3YpC_-IQ/s1600/a.png)
p = ± 3
sehingga persamaannya menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKTOl8W55ATa3M4RsYIznPHC6vK_SiWeHZsSSXe_WMmDTYYe29IMA3ARguFsxVTMK-F4Epvq7xTUWN7HIN-LWu7jqarsLAdtIjrKr6HJ-e_L7zwFaZ_X8gwCehTNydtkqElSaPjz6MR18/s1600/a.png)
Titik pusatnya = (- ½ .6 , - ½ .10) = (-3, -5)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMPNb26XoLNILfXkMCcm8AOL9AYAS3LKl1iGotWG4LSZM9PQ2RTwKeNXEJS526jBESiKl05sQKEsVLBobiQt0xRSa9YRk1WJXNNgE1D_LAC0PcYKqWB7NkDGmE2C0xF_OEk5vD1zjYm9o/s1600/a.png)
Titik pusatnya = (- ½ .(-6) , - ½ .10) = (3, -5)
Jawaban: E
9. Persamaan garis singgung melalui titik (5, 1) pada lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU3ivM7Q2a3dQaLnFQB2qQJgY5eyx9G8TU-1ImM1PyQ9O7GpqAW90l4H-BohokZFmqcYooA4GxoiNrcAgsuW7DPYM5qVRrSnEk4iN_J0463NVOvLcXJhMsimSE8FXjwHcyYdWbWqt8-6w/s1600/a.png)
adalah ...
a. 3x + 4y – 19 = 0
b. 3x - 4y – 19 = 0
c. 4x - 3y + 19 = 0
d. x + 7y – 26 = 0
e. x - 7y – 26 = 0
pembahasan:
persamaan garis singgung terhadap lingkaran melalui titik (5, 1) adalah:
x1.x + y1.y + a(x1 + x) + b (y1 + y) + c = 0
5.x + 1.y + ½ .(-4) (5 + x) + ½ .6 (1 + y) - 12 = 0
5x + y + -2 (5 + x) + 3 (1 + y) - 12 = 0
5x + y – 10 – 2x + 3 + 3y – 12 = 0
3x + 4y - 19 = 0
Jawaban: A
10. lingkaran dengan persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyIBjfcxFepm7Vm3lXo7f7O0Wdy4SqLJni5FJ02A7n1XpEG7HySFhfhuXtdADtgSruAq9WRW2XOd7CdbZzx8939bwapJ1RpF2_ftoXHu_KRw02T-JLGBArH7P8D9NmTY4RIVNnkURXylY/s1600/a.png)
a. √7
b. 3
c. 4
d. 2√6
e. 9
Pembahasan:
Lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyIBjfcxFepm7Vm3lXo7f7O0Wdy4SqLJni5FJ02A7n1XpEG7HySFhfhuXtdADtgSruAq9WRW2XOd7CdbZzx8939bwapJ1RpF2_ftoXHu_KRw02T-JLGBArH7P8D9NmTY4RIVNnkURXylY/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj028PwxcOb716nJmycUlZMyXCBM391uxXaOLpkbRkPm1ALtpOR9mhNZGRliK1vbXxqX4jvt_xHn9eC-ah46kbvCjtowJN9rUQMc38Xdzq2J6LSpJ9B-5K8gQS1RweUZLJB7PD75rgFMJc/s1600/a.png)
25 + 1 – 20 – 2 + c = 0
4 + c = 0
c = -4
sehingga jari-jari lingkarannya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUC7N-GIqwRNYH-dZScGKeyesj11SRjbvTXCAVVJLd4tc9moF5Eibnvd-qGwuQBIHWmNPCHwPS04vlxtWQ0-Kn7VQr1kkK3sXqKIOXZEsLZOu-1M2VFwoczy3dZO1ODuw_7hONxhPfU1Q/s1600/a.png)
r = 3
jawaban: B
11. Lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBZQl6PojrpNlh7XC4zaAHe4ebSX_ROl7sCLOL_8bMyodU6X9NIqKHjk4-2BTL91zqc4m051LI1Zkt6LmlCU2d0-kt9dWvJSsVo47bEsT2zalYotylZMlyLv_ZQkWBsgcW33gq7hb3JbU/s1600/a.png)
a. (-2, 3)
b. (2, -3)
c. (2, 3)
d. (3, -2)
e. (-3, 2)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZKyYAFi0FUrx1SCDz45GvIWjLQyteMjpL5DE2MLmhtU2k_ZDwd7nEY-62VdU9QZo8aVtUdsU_Qp2hL6SAlw9ffW50Z-R-wyE9QzrB-ukcBhhFGLFbEYv3LDjzyXo7S07J1sGHt3m8AbM/s1600/a.png)
p = ± 2
sehingga persamaannya menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsDgUfLuQ6PgzlAlRS4hPB9mznXkTVTvTbBZg1jD90AY9iwrHBgh5fxtjjOfBr0qeRKpL0MxxJduuv9Ms_spjakzPjkqJyZZyQFCdx1AGiZ9CPSDf_yIbvxn0N_8fSF9WcLPKdR_t424A/s1600/a.png)
Pusatnya: (- ½ .4, - ½ .6) = (-2, -3)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0eWGfaD7rj-dZzIpbyUINP8tiDiNQR07_Az-LrAMQghPgY0AUWpzCwuZ3khF63fSV5dDTQcoVmPNtsdNK38n0cn4VxTw-yw7k3kMtTngRf9O1kfDS9wafOsaqb_c6RP9f2xrgl4BbYyg/s1600/a.png)
Pusatnya: (- ½ . (-4), - ½ . 6) = ( 2, -3)
Jawaban: B
12. Persamaan garis singgung pada lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhecl26g0scK315enpm9m-Y75bfPfp0CCMlJ-DavygouJjZAJpmZcSnvD_F1zNn_mEZhSaoF0-15T04Szl_5jssaMOKjCAoygPOgYFAAWuIi4XSQDB8Zv6y_WctsyapYvvUWlPVibzXVMc/s1600/a.png)
a. 12x + 5y – 41 = 0 dan 12x + 5y + 37 = 0
b. 12x + 5y + 41 = 0 dan 12x + 5y + 37 = 0
c. 5x + 12y + 41 = 0 dan 5x + 12y + 37 = 0
d. 5x + 12y - 41 = 0 dan 5x + 12y - 37 = 0
e. 12x - 5y – 41 = 0 dan 12x - 5y - 37 = 0
Pembahasan:
Pusat lingkaran: ( - ½ .(-2), - ½ .4) = ( 1, -2)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIW-A79-bmqBBO70XO2WJRaBobQbmZRUhmjS_EdRDmv51kBcCiocyIhgwUleBuYyvcsHa_5qqhuCvH9vC7rurLwBnXl5DwpDRAcawbYfC9Odhj7xPgCqg7ykswqtxjqurX4oz5EbHKzuU/s1600/a.png)
r = 3
garis 5x – 12y + 15 = 0 memiliki gradien m = -a/b = -5/-12 = 5/12 karena garis yang ditanyakan adalah garis yang tegak lurus, maka gradiennya menjadi: -12/5
persamaan garis singgung lingkaran dengan pusat (a, b) ; berjari-jari r; dan bergradien m adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhox_HDOF2QjsE6zzt0RwCiQQWmbKu1H3i5rkUAknG8OfqQB17qC9MAlNne2_BlTI_oLH9LIbVz5i2Uk58pCIiAFE7hfSIhOQtuUf_6Hgoe9C2BONWRHysYauM0MYnf7La8SV11ZeD92jU/s1600/a.png)
Karena pusat lingkarannya (1, -2); r = 3, dan m = -12/5 , maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw9aVYuimwrW8Yb1t_7G_nGH0SG7eh1kYBDBa483i8pFkSDBdg2jWQ5SRs2cGB71DpT1Fi5ItZZpjXSwBZPshyphenhyphenaYfM2hFb4lt215uJDm_gX2Lhoz4nelX5oDQQE8wt83djsNpzFOIUMww/s1600/a.png)
(y + 2) = -12/5 (x – 1) ± 3 .13/5 (kalikan 5)
5 (y + 2) = 5 .-12/5 (x – 1) ± 5.3 .13/5
5y + 10 = -12 (x – 1) ± 15 . 13/5
5y + 10 = -12x + 12 ± 39
12x + 5y – 2 ± 39 = 0
Jadi, persamaan garis singgungnya:
12x + 5y – 2 + 39 = 0 ==> 12x + 5y + 37 = 0, dan
12x + 5y – 2 - 39 = 0 ==> 12x + 5y – 41 = 0
Jawaban: A
13. Persamaan lingkaran yang mempunyai diameter AB dengan A (-2, 2) dan B (2, -2) adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcJyjG06dkMAoc4t44C3zXo-Ww9VFtm1jaRxI4b_qPwJzl6ii7ilX43YJFB7OIko_tN1Thop35PDqTHKFwIUNYw1ohPq2Dj5U1OKXCdBA17tkL5_RN5Te47sHYGy_oDvMf4ewR_d1rWHU/s1600/a.png)
Pembahasan:
Jari-jari = ½ diameter
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimHal7JUNr9SoAHyr2daX3adsWR1iFd5QrvdaPIaoLhegQbHDDkgU_as2-mGZ35VBUq7bt2ZrD5JANBmKOosMkizJ5Y_KDBmv3qPrHCADSZafDgc9eabLPOkv59LJPhUb1V7fWQLEItEs/s1600/a.png)
r = ½ √32
r = ½.4 √2
r = 2√2
pusat lingkaran:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfokVARpl_nGg07-4-C8lnhsOEHcUXlXJh1Z0zjC-Vf4kIrwzTRl23sRVi7xCVabD-QVs7xPrn4B2OwX_sUmZqPQK5ox0iRzwI9yzz8-47Bk25NHZNGPvUpx74zs9SANxvNuwMwHba_hQ/s1600/a.png)
persamaan lingkarannya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1U1veRz4nCUtN3n0JO1E3lCUhCJU220Qgk8dc9gwm2mQ0MXNO4Vq8CaotIn9qugkt1alNeEHCw9MRpFjBW5M79qCOZ5Egl-4ciEO0x3wPBQ_SRmjSZxb-zkY98Jt2zpPUICKERnRDBQo/s1600/a.png)
jawaban: C
14. Garis x + y = 2 menyinggung lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMh16q7U-ywCo8ktoOGNSrVDbRCFWtuaYONGXSNFoQQo4n5s4nzRIxQujQd1Ua2KSg7l-b80y1hmBVuTahORdrCNcH-orVJOIRGX465QjxOUk7K2R_g9KHP0vJUIz8ENRZEumkMofyfhw/s1600/a.png)
a. -8
b. 4
c. 6
d. 8
e. 16
Pembahasan:
Pusat lingkaran = (- ½ .(-6), - ½ (-2)) = (3, 1)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj38lHEtSrvtDM7ika3IghZsovi3m20efY7yZlpqX94pSunK-Q_SAXhp7ks3ThzvWNDH5zuwnFbKV_e822ewCjJwCE2gdHJxxi0kzRiodLwcW0k9S66KCPv0lGooBNrB-DUTRtYq8QoEgw/s1600/a.png)
Jarak titik pusat (3,1) lingkaran dengan dengan garis x + y = 2 atau x + y – 2 = 0adalah r, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ_2W3VJ_JExaFQk0lPfFdCUtOv8liBPXzMNOPTANqZE67wY3DuL6oFhCduARpY24xdLxadCGk1lhrZzVJPt4_VIL3_8S4nIERnlH09s01fLOWyCXGXx_UJ-JBlu9FXdy_USjwU3oZzo0/s1600/a.png)
2 = 10 – q
q = 8
jawaban: D
15. Jika lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6m5gS-0xhIJkLZnRk2-ud2VQ1khXuR4WgPIQU0BcU4-5JoLvVTILtamVXj3crnOQw5vz7MXBlC28ZYg4_Dy7BtGiEFhzbcA_axbtwvAdpMcj2UiYjsNztTqsAena8hOn4qnsVHcpFaTc/s1600/a.png)
a. 0
b. 4
c. 5
d. 9
e. 13
Pembahasan:
Garis garis y = 1 – x menyinggung lingkaran, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHf7jWvRAbmOH_2o159OxuehiwnZQU66c8jlZT8eVfXlDqB_nvlkbS07WSKynaSu2fRXhW-g7NGi63OmhvYGrR1Bv_Eg4Pd0ns-3JFBgxwaVgM5o3FmIgtxI0LCRwjz5HYCK0nbInu2qI/s1600/a.png)
Syarat menyinggung adalah D = 0, maka:
0 – 4. 2. (-5 + c) = 0
40 – 8c = 0
8c = 40
c = 5
Jawaban: C
16. Persamaan garis singgung melalui titik (0, 5) pada lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWehpgf3UzcYvTvGEGnP9-xjFgQjT-fNM_Ge_b4A_-61eRWIHEX0YXgVzH8GGGS-fAQafRCc3bvYfMTe_5WXw6WSPlHMNqRQWjoPiOnh7CBq0Qy4IrTdT0-RUckfMVVHPR0kxNhrvDiGA/s1600/a.png)
a. 2x + y = 10 dan -2x + y = 10
b. x + 2y = 10 dan x - 2y = -10
c. x + 2y = 10 dan x - 2y = 10
d. x + y = -10 dan 2x - y = 10
e. x + 2y = -10 dan x - 2y = -10
Pembahasan:
Kita subtitusikan titik (0, 5) dalam
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWehpgf3UzcYvTvGEGnP9-xjFgQjT-fNM_Ge_b4A_-61eRWIHEX0YXgVzH8GGGS-fAQafRCc3bvYfMTe_5WXw6WSPlHMNqRQWjoPiOnh7CBq0Qy4IrTdT0-RUckfMVVHPR0kxNhrvDiGA/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOAWcctpAES5H6ZENUNb58XtiyP4uYW7JCJTnzvjhZq5prmg_wVh624lA39yqG-OJiXtn1Hel1Lr3SQWKDBWVNMDu1_RHt2tm5apsQi_gMMqiWOcW2amsJDRpVb3_MVN0A8AAVz0_0D8Y/s1600/a.png)
Persamaan garis yang melalui titik (0, 5) adalah:
y – y1 = m (x – x1)
y – 5 = m (x – 0)
y = mx + 5
kita subtitusikan y = mx + 5 pada persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWehpgf3UzcYvTvGEGnP9-xjFgQjT-fNM_Ge_b4A_-61eRWIHEX0YXgVzH8GGGS-fAQafRCc3bvYfMTe_5WXw6WSPlHMNqRQWjoPiOnh7CBq0Qy4IrTdT0-RUckfMVVHPR0kxNhrvDiGA/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_JcraqKPI0loJGy_0dn6Yk7zC0wVBujGkvoGlx-Kt4QKFq45IUPS2kCK9K6XQGJ5P43nTOeEeAK3C7_re_zWXAtyoMeDXc1U2VrcguVB0Oe-BuqyzK-f-NP_2BN9tt9S0CgDgrTtPlJA/s1600/a.png)
Karena y = mx + 5 menyinggung lingkaran, maka D = 0
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizeHkImesGEO56M2krKEGj-2rQfWeWrOYPxsrDixj5SEkU6cQe7pf2mGIloBbRmYp_0fg7ZjMPhPtH1Gx0-5Frx6xpdyJsP3BR5hckr3AmSfr9nldHfmYOiu1tjz9Y63ZZ5VgW8iTMOdM/s1600/a.png)
m = ± ½
- jika m = ½ maka:
2y = x + 10 atau x – 2y = 10
- jika m = - ½ maka:
2y = -x + 10 atau x + 2y = 10
Jawaban: B
17. Supaya garis y = x + a menyinggung lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhJziGN12pUUuvYCVzlycjf2VVTSoGifgWdu97bDV_6lDYMAsBpbCqvw3dpV66B_xMrXbZRdekgNZSmBrawaeRHAn9YrYuVMEk08LiF9fcz3n3vjEECCcquMj_jym-CL-5IV5_EOQFijo/s1600/a.png)
a. a = -6 atau a = 1
b. a = -5 atau a = 2
c. a = -1 atau a = 1
d. a = -6 atau a = 2
e. a = 6 atau a = -2
Pembahasan:
Garis y = x + a menyinggung lingkaran, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw4sFR_1uNcjI4hhGvihkx0tBIZmqE5xChrvi0qBHTQEJc0nLxtZTTOgpwwMuetyMOYUYW7byQUwx31qMxhCedLGOD7W7OFozJEUinhqvZfQw52BEtAVTIMxuB9cqb9ihh-OOQ8s037ws/s1600/a.png)
Syarat menyinggung, D = 0
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeyKOXi79bZuNf2jcxpiH7G9YbQcJPCx1_TC_BmuNxMnhuSvyEDlbQhSU4AthA5b2nEGgfcMHLnReXNTF9Fk5GBNbtnQdMCFyDHWi7vsLy57l_ykKBEi0ooDkb8ymb1AK9L-nzRBuIs9g/s1600/a.png)
(-a – 6) (a – 2) = 0
a = -6 atau a = 2
jawaban: D
18. Salah satu persamaan garis singgung yang ditarik dari titik A (0, 10) ke lingkaran yang persamaannya
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNuUaFN-wBFavSoeLOQOrfGIdnKlP4HqligvEw8LAAFtaaVHMHScDHLFQrhY4QyggfU42VzfYShncxhkHXsPvkq8AfcbN-F9EUz6J1cIP9p2tz1NKz4KuGWn305lXtI9gLMLLLLfwV428/s1600/a.png)
a. y = 10x + 3
b. y = 10x - 3
c. y = 3x - 10
d. y = -3x - 10
e. y = -3x +10
pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNuUaFN-wBFavSoeLOQOrfGIdnKlP4HqligvEw8LAAFtaaVHMHScDHLFQrhY4QyggfU42VzfYShncxhkHXsPvkq8AfcbN-F9EUz6J1cIP9p2tz1NKz4KuGWn305lXtI9gLMLLLLfwV428/s1600/a.png)
Persamaan garis singgung bergradien m adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgM2zMOUetjqxVFevZ5OAM9zPUXM7D0NDqudeaqmO6aBWqMXB4mb_SGU-MwEu74dqICWnp8wMk6Bol34F_HyvFkRAAGPfzsU5beGJIfnjfYZKvhWne7PgxWpuscq81pvMTuSTQA5w9ILMY/s1600/a.png)
Garis singgungnya melalui titik (0, 10), maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_Jl_UtRuhVTiBDOgXXR_mBfOvQNvJWBRPIcN7x92nVnyXVU_P545ODfftVrFblw3gAqd8ffgZfHwSRTJUuGkhHKCRwgv8UJRpdea5UyWc4rxadwqIMWL8_Vp6W2Y1aIiUZnkJ1Uvdvmc/s1600/a.png)
m = ± 3
Persamaan garis singgungnya menjadi:
- jika m = 3
y – 10 = 3 (x – 0)
y = 3x + 10
- jika m = -3
y – 10 = -3 (x – 0)
y = -3x + 10
Jawaban: E
19. titik pusat lingkaran L yang berada di kuadran I dan berada di sepanjang garis y = 2x. Jika L menyinggung sumbu y di titik (0, 6) maka persamaan L adalah ..
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQJGJuC1L4kQuucmepmwK7kMhoSy2Q2qG1QIDFAwoUr2vJdOckv-ha61rjbsSQr_4nafv7DQ_8aiEVjIXGMlH1US8ExGF8ZieTLnOw4bHp84mEHQfykDqeU-4oWe6DXLcCR6elKqygVmU/s1600/a.png)
Pembahasan:
Ketika y = 6, maka y = 2x, maka x = 3
Sehingg pusat lingkarannya adalah (3, 6) dengan jari-jari = r = x = 3
Maka, persamaan lingkarannya menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigeXrI5dpMKrf_HzdRmmgOcsUY4RI6O7pFtFVPLPxxMu3pRGF4NhE3jKDgsxCtsY9Pi015iVeFQDO584hL7zi9G-64uI3rlIGdFTSzvyE4-UVuVfkplZa_59_TwnuLgztCwva_7_era80/s1600/a.png)
Jawaban: E
20. Lingkaran yang sepusat dengan lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBgNiLHxcJoucgkFIHWVXS66fnnOl19q8BAx0W-ROQpBXVvHolH5WkdfjcgracWQM7PkLW502ABWXRaREiAPGgzAKD_G6ki0fNSkcrlOMpfyhI6M1I3hGPFbZwQ_zdTAEAuGoMsgAGrFE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp7G77VBrVaAlaPy2A1iGfu2qz4T_jQyz3cVLyx0QZ61NzRPb53xSSS2uOrJe7x-CTc-Nd15pVCm_RIswwALMb7SlONjWuEWsW-QVNmV8eB2Eiz7AgKgUqQHmbUZAypYWnSki0XemT5pE/s1600/a.png)
Pembahasan:
Pusat lingkaran = (- ½ .(-4), - ½ .6) = (2, -3)
Lingkaran menyinggung garis 3x – 4y + 7 = 0 maka jari-jarinya adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn7cClJfEIYQgb1ZwJIG42Ad-SurwmrlhiS1p0KIuhr0vK1IbuVk-GCRf5xRmC7UpZUKPTfzlh9o9Z49hwk8QA6lLb0VnrCMi1bY3zBIHG1cQfLxUpnk-HTuKL88H2x48tqxu1IT29hjs/s1600/a.png)
r = 5
persamaan lingkarannya adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGEgUM51ysiIbBP8UQMeh4fKQ-S5lmz1K47gETV7Dibq4ewdhsR8rWZq6-a8N5BN8a97m2Fg8tGESfdMquOFa1m3eb9R_PCtE9Td7Jg7FVZBXe6rdmFBhWT5dKy3DdX3Jr1Zc5_ud7m_Y/s1600/a.png)
Jawaban: A
21. Jika A (1, 3), B (7, -5) maka persamaan lingkaran yang mempunyai diameter AB adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_pW5jm8OXF12s5F2ep7Pk0KG0-m6lsR5XXMK7Af7PL2UB48CGDPnrPzzCmXfQ7usQPtOIqrXZrGUSz2FmYI1Yn4UrEmdb9M0lmyt81YIGcHWBW1wBMbxS9hYyBS3nUrf-XR9C1JXzUb4/s1600/a.png)
Pembahasan:
Titik pusat:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKgdW6Vd2j2HlM-Wuu345THWt1_ZezfBKt_wuFgYpxRnmAy_BR-7HsBQ1WMfDz2Y3vmKxzdq6Y-3VrqLS8e1nIbQ_aUGwUd7MY7vPeWBxWS6is-ReyQwr4UKETHrEd4EhVouulhLmS-fY/s1600/a.png)
Panjang jari-jari sama dengan jarak A ke B atau B ke titik pusat:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqMeCK53z7OCMCTsCv7puyn4UrTJaDBDJete6fIcuLZEnoM7bdgeNElGa5Jp-LZKYnUX9CLiB1Hoj-RnvEwv8vsK83z64JGLvHlnNP2s4XKy_2TVn5rS4jS_5mBE67e2DhjOOUoqfYf0Q/s1600/a.png)
Jadi, persamaan lingkaran dengan pusat (4, -1) dan jari-jari 5 adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8NQ0TRMmbeKtXDj63zNofUiDmwq06fx7li-htKTBY4zaQTdkCs7pHxpvPAhN0l41c62k9OKhw1qHr27Tdf-P2gwU-bE66Vto2h_NpB3LYRBIJ5cEina7_PO9d3xfwHvm2uztlq0mtxOg/s1600/a.png)
Jawaban: A
22. Diketahui suatu lingkaran dengan pusat berada pada kurva y = √x dan melalui titik asal O (0, 0). Jika absis titik pusat lingkaran terseut adalah a, maka persamaan garis singgung lingkaran yang melalui O adalah ...
a. y = -x
b. y = -x√a
c. y = -ax
d. y = -2x√2
e. y = -2ax
Pembahasan:
x = a, maka y = √x = √a sehingga titik pusatnya adalah (a, √a)
persamaan lingkarannya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRnfhydBG5zBLC6rLzw3E2rsh8t2EdMQH4vNr0uCqECbS3J7gTR4112D7CllvL5qr7tS23Iy-bdiNHCG96fATAWILNCchyphenhyphenCxGpA933FM2tgTVEOEKOfpKkSwkhVMzUWanKkMr8hV5daN8/s1600/a.png)
Lingkaran melalui titik O (0, 0), maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtl5bCOQ7Yr-cuuGP6aTei2CziNMyWk_OxUQ1bbCRx_yl2kc3nX7NBvRgZmHO69OZ1mvlFt9w8a0aEIFDhSEVin6BdB5W57wb_qdajMsFjC2tpCz6aeGR609lMvqGALv6moZSbzLlQmyE/s1600/a.png)
sehingga diperoleh
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6YS0wXMTvS8ul_A3m0Ub4LoS0wBXtb2XJie22AfhPx5xC0Qg3pfB3u0U3VPKj_vuxBCgdk4JiP1DN_P8LNo-80oe85TDBhbNCteto_JHywKag-2AftRnZaacpILZzOEMCMZ_IUI0Co-w/s1600/a.png)
persamaan garis singgung lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXQsOW7sX6WUnRvvQRKJ-6H-0Peis8kEbiubUnHb1-UbRz261niZ6ACGIv8UGL7GNtETb9gguKLUsLXfGJMlD-JVQ6FLIVlXu5qksLgllaWRPUvto0_6JqE5pvTX4nO9L6817PbEjdK9g/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8V4hJ1ytW9QlBu-YUEOTyPMdq2GqvXXOo1m-M9GB3oroepzigsUdio_SuEZhOR6kt_mBgreihoW8_P6GoigKqiWn9zS1bpWSWhuug2bM9ePoP_Ix6WhyUosM7K-FBxO3GYmaZpAx7TPs/s1600/a.png)
Jawaban: B
23. lingkaran
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhxIL_2H3QLFQRCy8BPiAd6skFCyAXEh3XU3YMUjpOlo1TqOpf5OBEB603PJFJsdD9dD-XJPdZ5imnVA1TAoOGugmuPxkwPTiY_4o0s7Do28XOJEx3Q3W3QY2zCL1ypIWLR8nVQrNJJZg/s1600/a.png)
a. 10√6 – 15
b. 10√5 - 15
c. 8√6 - 10
d. 8√5 - 10
e. 15/2 √6-10
Pembahasan:
Pusat lingkaran = (- ½ . (-2), - ½ . 6) = (1, -3)
Persamaan lingkaran dengan pusat (1, -3) dan jari-jari 5 adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgujyuKPbxA55-CIAY4JGsAF3ychVr132w4vzmbhCP1vE926mJhOLlnJU_3IH0f0WD2jBeem6cmTgzW8V1AeFyjE-AxJl601qH40WfA3Ct9Ckpnz-OCeU1zBvgo3R9u8Kol1fvajwjvStY/s1600/a.png)
Lingkaran memotong sumbu x positif, maka y = 0
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmT4t94jWjg5Ijk8CGjCVqyX2uJtvscyXjALchmSF-MN1w9nEQXSWo8pOgYKERO6iLJSj9VP9G6kLtz3nIUedwyjPKjNOA_rb2r-Bqt09Vtn8QoJCjn4l06J0llh2D7kFgSEj40d-Pg14/s1600/a.png)
x – 1 = √16
x – 1 = 4
x = 5
a = 5
lingkaran memotong sumbu y positif, maka x = 0
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1CsGB9HzsHJB6sud_SFLKzM32lmlUEen2AFtL5tVa4QdRkCkPmnCcO61hi881Yz5saUNSoDxY0QPUJa9o4GTwfw4z3Gq0zwPGJxmx43_n_G-RPuIgZ3aSAQ7NTaXkNFLCIX2SX-oGh2s/s1600/a.png)
y + 3 = √24
y = √24 – 3
b = √24 – 3
jadi, nilai ab = 5 (√24 – 3) = 5 (√4.6 – 3) = 10√6 - 15
Jawaban: A
24. Jari-jari lingkaran pada gambar di bawah ini adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFq0INRk-Jw9ZEt_rTdpktEOZiWbIO2dsnVVJ8x6cukuCrC694f6InvfyHi8PYPifM5u8-ex2tERH06e2aF9qBOeyKwx5dmfdoFKAsG9DBR0mb8bWrnZhmoioM72o1puD3XkHZ2OhHaQc/s1600/a.png)
a. √3
b. 3
c. √13
d. 3√3
e. √37
Pembahasan:
Bentuk umum persamaan lingkaran adalah
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio2m7zhNyA6N-gQ4AKfrkQbLyvIVODpUIiu_HhN4iSzy4TUYJIpEu96iSAiTKQZPIQBVioF2YLOUelsqvIrtncPDwSgmwy6e3sMePMUR7_9byQ5D2bxinJP3vI4KRvJj5x6_3uHwwE8gs/s1600/a.png)
- Lingkaran melalui A (5, 0), maka:
5A + C = -25 ... (i)
- Lingkaran melalui B (0, 5), maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVf-BircrG5njzOp_BB_3FgrKwKbIEeLjeMSekDCUDFMN8IJkJnTcks3g4r0iFEvzdx7KFwxktaGAVLAI8wOV9jEHtYeP_1BRnaCT7pdPE_x1wE02fRK2n7zswuYzoDy-5twRExHDBSH0/s1600/a.png)
25 + 5B + C = 0
5B + C = -25 ... (ii)
- Lingkaran melalui C (-1, 0), maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDPfpoK0I8DnALsDpwE3-SN4680ui4Kv3YvfkwOlBzVCAsHUQYkkTleVEls-BhixPHCGPW2b8iDWWmGjfux2SVG-ss2txhdIg7-LBWGyX1JZBClJljSFyKSajo46W4CE81NmXrET29BKA/s1600/a.png)
1 – A + C = 0
-A + C = -1 ... (iii)
Eliminasi (i) dan (iii)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjl_cNqwv0IlcyuVwof_Bfwghy31r9Uvoi0naDJGIVIvnWwHJUKztqIoBUa7Qx032oAmSu3g5zsBqpqG_VQhuA2t0OJZTQTryULNjaWwS2u-3BaJQA6R8cbbKqJX59pbH5JP2TOS_dVwZ4/s1600/a.png)
A = -4
Subtitusikan A = -4, pada persamaan –A + C = -1
-(-4) + C = -1
C = -5
Subtitusikan C = -5 pada persamaan 5B + C = -25
5B + (-5) = -25
5B = -20
B = -4
Sehingga persamaan lingkarannya menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil0y66ueYF6FBGxThworztkG16b1_SDyrHj_rdT7UrtWaDFFoNwjkcZEt2NrIZV3UVKFxgWxCrABBikJA6KjJqFfvaCJzTbvs-AepUycIY7w7Dy9va-BmUziyRV2-jWGSyoDGka4Y2km8/s1600/a.png)
Jari-jarinya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZdemv0Ggcpsfgl06qP93jNa_i37pUWhPmqTpJVCHPn0ZrzfFVJY7T1CUlQFo9FtxDs0hSNy8YPSCgxJdRP9dy9yOUBazs8jDD0K3-TGxK3pu7hdntL00nQ5fYhUOREX9tXe2RLGrH2mE/s1600/a.png)
r = √13
Jawaban: C
25. Salah satu garis singgung yang bersudut 120 derajat terhadap sumbu x positif pada lingkaran dengan ujung diameter di titik (7, 6) dan (1, -2) adalah ...
a. y = -x√3 + 4√3 + 12
b. y = -x√3 - 4√3 + 8
c. y = -x√3 + 4√3 + 8
d. y = -x√3 - 4√3 - 8
e y = -x√3 + 4√3 + 22
Pembahasan:
Jari-jari:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuNnZ8U0tjS-lP1SH3m-OcGzFTS7gBRRnyfPUJAnSL5CEZhICfCWOxaOLTDbt4Nb68k9KxQadwQ1LQWVm6nzpKTYOqEIKFG0oPBsh7MWuSFunzNJsS2rpJb3Q7Uxy5oExA_efzNWaUJ3U/s1600/a.png)
Titik pusat:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYw8AUmT6iH10oUlhhydvQ6hbBoEysZQKZkbU5veJTAGICoL1VthPLtUbYgJt2DtuuNpeAq3uxx8jalTC-oVH4862VawXWiwN4zJMaNvkNaa22YrvsR5u5JrVhsqn5ioppNqbTeaF7Mss/s1600/a.png)
Persamaan lingkarannya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD3BL7DjHZ24rLppUSDBZz-covl9I5S3aHRBl2z7RaD0BA2wONqYsUA-z_IfT1yRUy_10E2NsiVRtwlRCd0HN_av_MujginfbaRjsbS1Difw2x_f9hApIS0p18wlhS-aY4boEU0WgEwJg/s1600/a.png)
Persamaan garis singgung lingkaran:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyuKubx1pjH1CIQ-qQR5Q0hBcLANorGOaqys1YMSrQpeMF2aUlEDlyrdIXfBiWTuESlA3yUQA3ZS3P7KrvxuIv8XWIREOxwQ9r9onzFoQQybpOwkm6lcaLAn4SdNh6iXv6N1ls1GK9zRE/s1600/a.png)
Perhatikan gambar garis singgung yang dimaksud:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiV_ubdfPj6Bn7h8xsjsdwcwjDBBGlbJKxfJE-vFob9FYDvbn2UufSLUYlJ5lH_m-zp0jbbYvNXHMt8OwdcALTLhiTbBH6muepCxCY5cZgYLpD63ASJcRDZ6WcL8cgyVPng9iCtPX-vF0k/s1600/a.png)
Berdasarkan gambar di atas, gradien garis yang dimaksud adalah y/x = - √3 /1 = - √3
Maka persamaan garis singgungnya (i) menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzUVKedfBCSiInzlzgsrklXFQ5mZDD1KO3VTzsIreBGOnX3r4Gq4q4UsCBhjsCzCyxUkOcsLE_zhSLPo39m1W0iRhdyzU28MByTW4hY6XtOhvrCr4pygRr4xkKNgpyo9D0M2uISNqFZXE/s1600/a.png)
y = - x√3 + 4 √3 ± 5√4 + 2
y = - x√3 + 4 √3 ± 10 + 2
y = - x√3 + 4 √3 ± 10 + 2
y = - x√3 + 4 √3 + 10 + 2 = - x√3 + 4 √3 + 12
y = - x√3 + 4 √3 - 10 + 2 = - x√3 + 4 √3 - 8
Jawaban: A
Gimana nih adik-adik? setelah belajar bersama kakak, makin paham atau makin bingung nih? hehehe... semoga bermanfaat ya, jangan putus-putus latihannya...
Sangkyu kak...
ReplyDeleteContoh soalnya komplet dan sangat membantu...
Keren
ReplyDeleteTerima kasih
ReplyDeleteSangat bermanfaat
Semoga dibalas dengan kebaikan yg tak terbatas
makasihhhh
ReplyDeleteTerima kasih banyak ^^
ReplyDeleteSama2.... semoga bermanfaat dan selamat belajar.... 🙂
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