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Question

A circle touches x-axis and also touches the circle whose centre is (0,3) and radius 2 units. The locus of the centre of the circle is

A
a director circle
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B
a parabola
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C
an ellipse
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D
a hyperbola
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Solution

The correct option is A a parabola
Let locus of centre be α,β then according to given, if r1,r2,are radii of circles then C1C2=r2±r1
(α0)2+(β3)2=|β±2|
α2+β26β+9=β2+4+4β
and α2+β26β+9=β24β+4
α210β+5=0 and x22β+5
x210y5 and x2=2y5 both are parabolas but x2=2y5 does not exist
Ans: B

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