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Question

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

A
(2,2)
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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)

As the circle is touching the xaxis at (3,0),
let the centre of the circle be C(3,k)
Radius, r=|k|
Equation of the circle is (x3)2+(yk)2=k2
Above circle passes through (1,2).
Then, (13)2+(2k)2=k2
k=2
Hence, equation of the circle is (x3)2+(y+2)2=4
Clearly, (5,2) satisfies it.

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