Question

find the equation of the tangents to the circle x^2 + y^2 = 9 which are parallel to 3x + 4y =0 .​

Answer 1

y = mx + c is the tangent to a circle x² + y² = 9 if c² = 9(m² + 1)

Given tangent is parallel to y = -3x/4

From here, m = -3/4

c² = 9((-3/4)² + 1) = 225/16

c = ± 15/4

Tangents required:

y = -3x/4 ± 15/4

3x + 4y = ±15