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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 parabolaLet locus of centre be α,β then according to given, if r1,r2,are radii of circles then C1C2=r2±r1 ⇒(α−0)2+(β−3)2=|β±2| ⇒α2+β2−6β+9=β2+4+4β and α2+β2−6β+9=β2−4β+4 ⇒α2−10β+5=0 and x2−2β+5 ⇒x2−10y−5 and x2=2y−5 both are parabolas but x2=2y−5 does not existAns: B

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