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Question

The circle passing through (1,2) and touching the axis of x at (3,0) also passes through the point

A
(5,2)
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B
(2,5)
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C
(5,2)
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D
(2,5)
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Solution

The correct option is C (5,2)
Let the centre is (3,k) and radius is k


The equation of circle is
(x3)2+(yk)2=k2
The circle passes through (1,2)
(13)2+(2k)2=k2
k=2
Therefore, equation of circle is
(x3)2+(y+2)2=4
Cleary, (5,2) is satisfyng the equation of circle.

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