Question

A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)² + y² = 16 and x² + y² = 1. Then 

(A) radius of S is 8 

(B) radius of S is 7 

(C) center of S is (-7, 1) 

(D) center of S is (-8, 1)

Answer 1

(B) radius of S is 7 

(C) center of S is (-7, 1) 

Given circles

x² + y² - 2x - 15 = 0 

x² + y² - 1 = 0 

Radical axis x + 7 = 0 … (1) 

Centre of circle lies on (1) 

Let the centre be (-7, k) 

Let equation be x² + y² + 14x - 2ky + c = 0 

Orthogonallity gives 

-14 = c -15 ⇒ c = 1 … (2) 

(0, 1) → 1 - 2k + 1 = 0 ⇒ k = 1