Mathematics - Application of Derivative Question with Solution | TestHub

$\Rightarrow \frac{dy}{dx}=-\frac{x^{1/2}}{y^{1/2}}$ $\therefore \left|{\left(\frac{dy}{dx}\right)}_{(\alpha ,\beta )}\right|=1\Rightarrow {\alpha }^{1/2}={\beta }^{1/2}$; also ${\alpha }^{3/2}+{\beta }^{3/2}=a^{3/2}(\because (\alpha ,\beta )$ is on the curve $)$ $\therefore \alpha =\beta =\frac{a}{2^{2/3}}$, there is only one point