Mathematics - Application of Derivative Question with Solution | TestHub

Taking $\log$ and differentiating both sides, we get $\frac{dy}{dx}=\frac{ny}{x}\dots$ Length of sub-normal $=\left|y\frac{dy}{dx}\right|=\frac{n{y}^2}{x}=n{a}^{2-2n}{x}^{2n-1}$, which is constant when $2n-1=0$ $n=\frac{1}{2}$