Question

Find the equations to the tangents to the circle x² + y² - 6x + 4y = 12 which are parallel to the straight line 4x +3y + 5 = 0.

Answer 1

Any straight line parallel to the given one is

4x + 3y + C = 0 ......(1)

The equation to the circle is

(x - 3)² + (y + 2)² = 5².

The straight line (1), if it be a tangent, must be therefore such that its distance from the point (3, - 2) is equal to ±5.

The required tangents are therefore

4x + 3y + 19 = 0 and 4x + 3y - 31 = 0.