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Question:

A circle S passes through the point (0,1) and is orthogonal to the circles (x-4)²+y²=16 and x²+y²=1. Then what is the radius and centre of S?

Centre of S is (-4,1)

Centre of S is (-8,1)

Radius of S is 8

Radius of S is 7

Solution:

Given circles x²+y²-8x=0, x²+y²=1
Let equation of circle x²+y²+2gx+2fy+c=0
The circle passes through (0,1) ⇒ 1+2f+c=0
Applying condition of orthogonality -8g=c, 0=c
⇒ c=1, g=-1/8, f=-1
r=√(1/64+1) = √65/8; centre(-1/8,-1)