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) $y^2 - x^2 = 2xy$ (4) $x^2 - y^2 = 2xy$
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) $y^2 - x^2 = 2xy$\\
(4) $x^2 - y^2 = 2xy$