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

Question

TestHub · Accepted Answer

Plotting the diagram of given data we have,

Now to find locus, let centre be $(h, k)$ . According to question

$|O M| = |O N|$ distance

$\Rightarrow$ $|h| = \frac{|h + k|}{\sqrt{2}}$

squaring both sides we get

$\Rightarrow 2 h^{2} = {(h + k)}^{2}$

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

Replacing $h$ with $x$ & $k$ with $y$ we get

$2 x^{2} = x^{2} + y^{2} + 2 x y$

$\Rightarrow x^{2} - y^{2} = 2 x y$

Mathematics - Circle Question with Solution | TestHub