The poles of the tangents to the circle x 2 + y 2 = 4 with respect to the circle ( x + 2 ) 2 + y 2 = 8 lie on

Step-by-step solution

Given: x 2 + y 2 = 4 x + 2 2 + y 2 = 8 Equation of tangent at any point on the circle x 2 + y 2 = 4   is x cos θ + y sin θ = r x cos θ + y sin θ = 2     . . . 1 The polar of x 1 , y 1   w.r.t. x + 2 2 + y 2 = 8 x x 1 + y y 1 + 2 x + x 1 - 4 = 0 ⇒   x 1 + 2 x + y 1 y + 2 x 1 - 2 = 0       . . . 2 from equation 1   & 2 , we get cos θ x 1 + 2 = sin θ y 1 = - 2 2 x 1 - 2 cos θ = - x 1 + 2 x 1 - 2   & sin θ = - y x 1 - 2 cos