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

Step-by-step solution

Given circles x 2 + y 2 - 2 x - 15 = 0 x 2 + y 2 - 1 = 0 Radical axis x + 7 = 0 ......(i) Centre of circle lies on (i) Let the centre be - 7 , k Let equation be x 2 + y 2 + 14 x - 2 k y + c = 0 Orthogonallity gives - 14 = c - 15 ⇒ c = 1 .......(ii) 0 , 1 → 1 - 2 k + 1 = 0 ⇒ k = 1 Hence radius = 7 2 + k 2 - c = 49 + 1 - 1 = 7 Alternate Solution Given circles x 2 + y 2 - 2 x - 15 = 0 x 2 + y 2 - 1 = 0 Let equation of circle x 2 + y 2 + 2 g x + 2 f y + c = 0 Circle passes through (0, 1) ⇒ 1 + 2 f + c = 0 Applying cond