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Question

A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is

A

A circle

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B

An Ellipse

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C
A hyperbola
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D
A parabola
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Solution

The correct option is D A parabola
Suppose the centre of circle be (h,k).
Since it touches the y-axis, radius of circle = h

Now (h2)2+k2=h2h2+44h+k2=h2
k2 = 4 h - 4.
Hence the locus of centre is y2= 4x - 4, which is a parabola.


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