The tangent to the circle x 2 + y 2 = 5 at the point 1 , - 2 also touches the circle x 2 + y 2 - 8 x + 6 y + 20 = 0 at the point

Step-by-step solution

Equation of the tangent to x 2 + y 2 = 5 at 1 , - 2 is x 1 + y - 2 = 5 . Let, this tangent touches x 2 + y 2 - 8 x + 6 y + 20 = 0 at h , k Then, h x + k y - 4 x + h + 3 y + k + 20 = 0 is same as x - 2 y - 5 = 0 ⇒ h - 4 1 = k + 3 - 2 = - 4 h + 3 k + 20 - 5 ⇒ 2 h + k - 5 = 0 and h + 3 k = 0 ⇒ h = 3 , k = - 1 ⇒ Required point is 3 , - 1