A circle touches the line L and the circle C1 externally such that both the circles are on the same side of the line, then the locus of the centre of the circle is
A
ellipse
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B
hyperbola
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C
parabola
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D
parts of straight line
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Solution
The correct option is C parabola Let the center of the required circle be C and C1 be p and P1 Draw a line parallel to L at a distance 1 unit from it, where r is the radius of the required circle Then CP1=r+1=CM ⇒ C is equidistant from the point P1 and the line parallel to L ⇒ locus of C is a parabola