Question

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

Answer 1

The equation of the tangent to the circle

x² + y² + 2gx + 2fy + c = 0 at (x₁, y₁) is

xx₁ +yy₁ + g(x + x₁) + f{y + y₁) + c = 0    ...(1)

Comparing the equation x² + y² – 3x + 2y = 0 with

x² + y² + 2gx + 2fy + c = 0, we get,

2g= –3, 2f = 2 and c = 0

∴ g = `-3/2, "f" = 1 and "c" = 0`

∴ from (1), the equation of the tangent to the given circle at the origin (0, 0) is

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

∴ `-3/2x + y` = 0.

∴ 3x – 2y = 0.