The centre C of a variable circle passing througha fixed point (a, 0), a > 0, touches the line y = x.Locus of C is a parabola whose directrix is

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x + y = 0

x+y=a

x−y=0

x−y=a

answer is C.

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Detailed Solution

C is equidistant from the point (a, 0) and the liney=x, so locus of C is a parabola with directrixy = x i.e. x – y = 0.

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