Roboguru

Persamaan lingkaran dengan pusat (-1, 1) dan menyi...

Persamaan lingkaran dengan pusat (-1, 1) dan menyinggung garis 3x - 4y +12 = 0 adalah...

  1. begin mathsize 12px style x squared plus y squared plus 2 x minus 2 y plus 1 equals 0 end style

  2. begin mathsize 12px style x squared plus y squared plus 2 x minus 2 y minus 7 equals 0 end style

  3. begin mathsize 12px style 4 x squared plus 4 y squared plus 8 x minus 8 y minus 17 equals 0 end style

  4. begin mathsize 12px style x squared plus y squared plus 2 x minus 2 y minus 2 equals 0 end style

  5. begin mathsize 12px style 4 x squared plus 4 y squared plus 8 x minus 8 y minus 1 equals 0 end style

Jawaban:

Ingat!

Jarak antara titik pusat lingkaran begin mathsize 12px style open parentheses x subscript 1 comma space y subscript 1 close parentheses end style dengan garis ax + by + c = 0, sama dengan jari-jari lingkaran tersebut yaitu:

begin mathsize 12px style r equals d equals fraction numerator vertical line a x subscript 1 plus b y subscript 1 plus x vertical line over denominator square root of a squared plus b squared end root end fraction end style

Sehingga jari-jari lingkaran tersebut dengan titik pusat (–1, 1) dan menyinggung garis 3x – 4y + 12 = 0 adalah:

size 12px r size 12px equals fraction numerator size 12px vertical line size 12px 3 open parentheses size 12px minus size 12px 1 close parentheses size 12px minus size 12px 4 open parentheses size 12px 1 close parentheses size 12px plus size 12px 12 size 12px vertical line over denominator square root of size 12px 3 to the power of size 12px 2 size 12px plus open parentheses size 12px minus size 12px 4 close parentheses to the power of size 12px 2 end root end fraction  size 12px r size 12px equals fraction numerator size 12px vertical line size 12px 3 size 12px minus size 12px 4 size 12px plus size 12px 12 size 12px vertical line over denominator square root of size 12px 25 end fraction  size 12px r size 12px equals fraction numerator size 12px vertical line size 12px 5 size 12px vertical line over denominator size 12px 5 end fraction  size 12px r size 12px equals size 12px 1

Ingat!

Persamaan lingkaran dengan pusat begin mathsize 12px style open parentheses x subscript 1 comma space y subscript 1 close parentheses end style dan jari-jari r dapat ditentukan dengan rumus:

open parentheses size 12px x size 12px minus size 12px x subscript size 12px 1 close parentheses to the power of size 12px 2 size 12px plus open parentheses size 12px y size 12px minus size 12px y subscript size 12px 1 close parentheses to the power of size 12px 2 size 12px equals size 12px r to the power of size 12px 2

Maka persamaan lingkaran tersebut adalah:

open parentheses size 12px x size 12px minus open parentheses size 12px minus size 12px 1 close parentheses close parentheses to the power of size 12px 2 size 12px plus open parentheses size 12px y size 12px minus open parentheses size 12px 1 close parentheses close parentheses to the power of size 12px 2 size 12px equals open parentheses size 12px 1 close parentheses to the power of size 12px 2  open parentheses size 12px x size 12px plus size 12px 1 close parentheses to the power of size 12px 2 size 12px plus open parentheses size 12px y size 12px minus size 12px 1 close parentheses to the power of size 12px 2 size 12px equals size 12px 1  size 12px x to the power of size 12px 2 size 12px plus size 12px 2 size 12px x size 12px plus size 12px 1 size 12px plus size 12px y to the power of size 12px 2 size 12px minus size 12px 2 size 12px y size 12px plus size 12px 1 size 12px minus size 12px 1 size 12px equals size 12px 0

 

Jadi, persamaan lingkaran tersebut adalah size 12px x to the power of size 12px 2 size 12px plus size 12px y to the power of size 12px 2 size 12px plus size 12px 2 size 12px x size 12px minus size 12px 2 size 12px y size 12px plus size 12px 1 size 12px equals size 12px 0

 

0

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