Question

If $a{x}^2+2hxy+b{y}^2=0$, then $\frac{dy}{dx}$ is equal to

Answer 1

Given that ,

$a{x}^2+2hxy+b{y}^2=0$

Differentiate on both sides w.r.t 'x'

$2ax+2hy+2hx\frac{dy}{dx}+2by\frac{dy}{dx}=0$

$(ax+hy)+(hx+by)\frac{dy}{dx}=0$

$\therefore \frac{dy}{dx}=\frac{-(ax+hy)}{(hx+by)}$