A circle touches both the y-axis and the line x+y=0.

Question

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

Accepted Answer

For centre $(h,k)$: $|h|=\dfrac{|h+k|}{\sqrt2}\Rightarrow2h^2=(h+k)^2=h^2+2hk+k^2\Rightarrow h^2-k^2=2hk$.

Locus: $x^2-y^2=2xy.$

Solutions · 1