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Question

A circle which made an intercept of 2a on yaxis and xaxis is the tangent to it. The locus of the center of the circle is

A
Hyperbola with eccentricity 2
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B
Hyperbola with eccentricity 3
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C
Ellipse with eccentricity 12
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D
Parabola with focus (0,2a)
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Solution

The correct option is A Hyperbola with eccentricity 2
Let the center of the circle is (h,k)
equation of the circle is
(xh)2+(yk)2=k2x2+y2+h22hx2ky=0
For y intercept of the circle
y2+h22ky=0
y=k±k2h2
length of the y intercept
2k2h2=2a
k2h2=a2
Locus will be y2x2=a2

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