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

1. $y=\sqrt{2} x$
2. $x=\sqrt{2} y$
3. $y^2-x^2=2 x y$
4. $x^2-y^2=2 x y$

Solution

Let $(h, k)$ is centre of circle
$\left|\frac{h-k}{\sqrt{2}}\right|=|h|, k^2-h^2+2 h k=0$

Asked in: BITSAT 2023 (Memory Based Paper 1)

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