Roboguru

Tentukan persamaan garis singgung pada suatu lingkaran  yang ditarik dari titik  diluar lingkaran.

Pertanyaan

Tentukan persamaan garis singgung pada suatu lingkaran begin mathsize 14px style x squared plus y squared plus 2 x minus 19 equals 0 end style yang ditarik dari titik begin mathsize 14px style T left parenthesis 1 comma 6 right parenthesis end style diluar lingkaran.

Pembahasan Soal:

Misalkan persamaan garis singgungnya adalah :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell m left parenthesis x minus x subscript 1 right parenthesis end cell row cell y minus 6 end cell equals cell m left parenthesis x minus 1 right parenthesis end cell row y equals cell m x minus m plus 6 end cell end table end style 

Lalu substitusi persamaan garis singgung tersebut ke persamaan lingkaran soal.

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px x to the power of size 14px 2 size 14px plus size 14px left parenthesis size 14px m size 14px x size 14px minus size 14px m size 14px plus size 14px 6 size 14px right parenthesis to the power of size 14px 2 size 14px plus size 14px 2 size 14px x size 14px minus size 14px 19 end cell size 14px equals size 14px 0 row cell size 14px x to the power of size 14px 2 size 14px plus size 14px m to the power of size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px m to the power of size 14px 2 size 14px plus size 14px 36 size 14px minus size 14px 2 size 14px m to the power of size 14px 2 size 14px x size 14px plus size 14px 12 size 14px m size 14px x size 14px minus size 14px 12 size 14px m size 14px plus size 14px 2 size 14px x size 14px minus size 14px 19 end cell size 14px equals size 14px 0 row cell size 14px left parenthesis size 14px 1 size 14px plus size 14px m to the power of size 14px 2 size 14px right parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px left parenthesis size 14px minus size 14px 2 size 14px m to the power of size 14px 2 size 14px plus size 14px 12 size 14px m size 14px plus size 14px 2 size 14px right parenthesis size 14px x size 14px plus size 14px m to the power of size 14px 2 size 14px minus size 14px 12 size 14px m size 14px plus size 14px 17 end cell size 14px equals size 14px 0 end table 

Agar garis menyinggung lingkaran, maka nilai D harus nol.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row D equals cell b squared minus 4 a c equals 0 end cell row D equals cell left parenthesis negative 2 m squared plus 12 m plus 2 right parenthesis squared minus 4 left parenthesis 1 plus m to the power of 2 end exponent right parenthesis left parenthesis m squared minus 12 m plus 17 right parenthesis equals 0 end cell row D equals cell up diagonal strike 4 m to the power of 4 end strike plus 144 m squared plus 4 minus up diagonal strike 48 m cubed end strike minus 8 m squared plus 48 m minus 4 m squared plus 48 m minus 68 minus up diagonal strike 4 m to the power of 4 end strike plus up diagonal strike 48 m cubed end strike minus 68 m squared equals 0 end cell row D equals cell 64 m squared plus 96 m minus 64 equals 0 end cell end table end style

Diiperoleh begin mathsize 14px style m subscript 1 equals negative 2 end style dan begin mathsize 14px style m subscript 2 equals 1 half end style

Maka, persamaan garis singgungnya adalah :

begin mathsize 14px style y equals negative 2 x plus 8 end style dan begin mathsize 14px style y equals 1 half x plus 11 over 2 end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Maret 2021

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved