Question

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

• A. $y=\sqrt{2}x$
• B. $x=\sqrt{2}y$
• C. $y^2-x^2=2xy$
• D. $x^2-y^2=2xy$

Answer 1

Answer: (D)

Let $(h,k)$ is centre of circle
$\left|\frac{h-k}{\sqrt{2}}\right|=|h|$
$k^2-h^2+2hk=0$
$\therefore$ Equation of locus is $y^2-x^2+2xy=0$