A pair of tangents are drawn from a point P to the circle x 2 + y 2 = 1 . If the tangents make an intercept of 2 units on the line x = 1 , then the locus of the point P is

Step-by-step solution

Let P ( h , k ) be the point from which tangents are drawn. So, combined equation of P A and P B is x h + y k - 1 2 = x 2 + y 2 - 1 h 2 + k 2 - 1 ∵ T 2 = S S 1 Putting x = 1 , we get, h - 1 2 + 2 k y h - 1 = y 2 h 2 - 1 ⇒ h + 1 y 2 - 2 k y - h - 1 = 0 where roots are y 1   &   y 2 and y 1 - y 2 = 2 ⇒ 2 k 2 + 4 h + 1 h - 1 h + 1 = 2 ⇒ y 2 + x 2 - 1 = x 2 + 2 x + 1 ⇒ y 2 = 2 x + 1