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CGP EDU Academic Team
Published on: August 14, 2026
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
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(b,c)Let the cirlce be
x 2 + y 2 + 2gx + 2fy + c = 0 ...(1)
given circles
x 2 + y 2 – 2x – 15 = 0 ...(2)
x 2 + y 2 – 1 = 0 ....(3)
(1) & (2) are orthogonal
⇒ –g + 0 = 
0 + 0 = 
⇒ c = 1 & g = 7
so the cirle is
x 2 + y 2 + 14x + 2fy + 1 = 0 it passes thrgouh
(0, 1) ⇒ 0 + 1 + 0 + 2f + 1 = 0
f = –1
⇒ x 2 + y 2 + 14x – 2y + 1 = 0
Centre (–7, 1)
radius = 7
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