Question

Find the equation of a tangent to the circle x² + y² – 3x + 2y = 0 at the origin.

Answer 1

Given equation of the circle is x² + y² – 3x + 2y = 0 

Comparing this equation with x² + y² + 2gx + 2fy + c = 0, we get 

2g = -3, 2f = 2, c = 0

⇒ g = - 3/2, f = 1, c= 0

The equation of a tangent to the circle 

x² + y² + 2gx + 2fy + c = 0 at (x₁ , y₁ ) is xx₁ +yy₁ + g(x + x₁) + f(y + y₁) + c = 0 

The equation of the tangent at (0, 0) is

x(0) + y(0) + (- 3/2) (x + 0) + 1(y + 0) + 0 = 0

⇒ - 3/2 x +y = 0

⇒ 3x – 2y = 0