Question

If $a{x}^2+2hxy+b{y}^2=0$, show that $\frac{d^{2}y}{d{x}^2}=0$

Answer 1

Given equation, is the homogenous equation in two variable , i.e, Passing through origin.

And its, $△=abc+2fgh-b{g}^2-a{f}^2-c{h}^2=0$ , which represents pair of straight line passing through origin.

So, for straight line , slope, i.e, $\frac{dy}{dx}=$constant.

Therefore, $\frac{d^{2}y}{d{x}^2}=0$

Hence proved.