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Question

Locus of the centre of the circle which always passes through the fixed point (a,0) and (a,0), where a0, is

A
x=1
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B
x+y=6
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C
x+y=2a
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D
x=0
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Solution

The correct option is D x=0
Let given points be A=(a,0), B=(a,0) and the center be C(h,k), then
CA2=CB2(ha)2+k2=(h+a)2+k24ah=0h=0

The required locus is x=0

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