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Question

A circle S passes through the point (0,1) and is orthogonal to the circles (x1)2+y2=16 and x2+y2=1. Then

A
Radius of S is 8
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B
Radius of S is 7
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C
Centre of S is (7,1)
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D
Centre of S is (8,1)
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Solution

The correct option is C Centre of S is (7,1)
Let the equation of circle be
x2+y2+2gx+2fy+c=0
It passes through (0,1)
1+2f+c=0(i)
This circle is orthogonal to (x1)2+y2=16
i.e., x2+y22x15=0
and x2+y21=0
We should have
2g(1)+2f(0)=c15
or 2g+c15=0(ii)
and 2g(0)+2f(0)=c1
or c=1(iii)
Solving (i),(ii) and (iii), we get
c=1, g=7, f=1
Required circle is
x2+y2+14x2y+1=0
With centre (7,1) and radius = 7.

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