Question

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

• A. $y=\sqrt2x$
• B. $x=\sqrt2y$
• C. $y^2-x^2=2xy$
• D. $x^2-y^2=2xy$

Answer 1

Answer: (A)

$y=\sqrt2x$

Answer 2

The correct option is(D): $x^2-y^2-2xy$.

Let the centre be (h , k)

So,

$|h|=|\frac{h+k}{\sqrt2}|$

⇒ 2 h 2 = h 2 + k 2 + 2 hk

Locus will be x 2 – y 2 = 2 xy