Tangents are drawn to the circle x 2 + y 2 = 16 at the points where it intersects the circle x 2 + y 2 - 6 x - 8 y - 8 = 0 , then the point of intersection of these tangents is

Step-by-step solution

S 1   :   x 2 + y 2 - 16 = 0 S 2   : x 2 + y 2 - 6 x - 8 y - 8 = 0 In this case, the common chord is the same as the chord of contact A B So, the equation of A B is 3 x + 4 y - 4 = 0 which is identical with x x 1 + y y 1 - 16 = 0 x 1 3 = y 1 4 = 16 4 ⇒     x 1 = 12 ,   y 1 = 16 ⇒   P x 1 , y 1 = 12 , 16