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Q.

A circle touches both the y-axis and the line x + y =0. Then the locus of its center is

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a

$x^{2} - y^{2} = 2 x y$

b

$y = \sqrt{2} x$

c

$x = \sqrt{2} y$

d

$y^{2} - x^{2} = 2 x y$

answer is D.

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Detailed Solution

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Let (h, k) is centre of circle

$|\frac{h + k}{\sqrt{2}}| = | h | k^{2} - h^{2} + 2 h k = 0$

$∴$ Equation of locus of (h, k) is $y^{2} - x^{2} + 2 x y = 0$

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