Question

Salah satu garis singgung kurva lingkaran x^2 + y^2 - 4x- 6y -7 = 0yang sejajar dengan garis 2y = 4x-7 adalah?

Answer 1

M = 2

x^2 + y^2 - 4x- 6y -7 = 0
(2x-4) dx + (2y-6) dy = 0
dy/dx = -(2x-4)/(2y-6) ; subtitusi dy/dx = 2
       2 = -(2x-4)/(2y-6)
4y-12 = 4-2x
     2x = 16-4y
       x = 8-2y ←subtitusi ke pers lingkaran

x² + y² - 4x- 6y -7 = 0
(8-2y)² + y² - 4(8-2y) - 6y -7 = 0
4y²-32y+64 + y² -32+8y -6y - 7 = 0
5y²-30y+25 = 0
5(y-5)(y-1) = 0
              y = 1 atau y = 5

saat y= 5; x = -2
persamaan garis:
y-y1 = m(x-x1)
  y-5 = 2(x+2)
     y = 2x+9

saat y= 1; x = 6
persamaan garis:
y-y1 = m(x-x1)
  y-1 = 2(x-6)
     y = 2x-11