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 center is :

Accepted Answer

Let the centre be (h, k)

So, $$\left| h \right| = \left| {{{h + k} \over {\sqrt 2 }}} \right|$$

$$ \Rightarrow 2{h^2} = {h^2} + {k^2} + 2hk$$

Locus will be ${x^2} - {y^2} = 2xy$

Solutions · 1