Mathematics - Application of Derivative Question with Solution | TestHub

$y_1=\sqrt{2}\sin \left(x_1+\frac{\pi }{4}\right),\frac{dy}{dx}=\frac{y_1}{x_1}$ where $\left(x_1,y_1\right)$ is point on the curve (tangent passes through origin) $\begin{array}{rlr}& \therefore \frac{y_1^2}{x_1^2}=2{\cos }^2\left(x_1+\frac{\pi }{4}\right)=2\left(1-\frac{y_1^2}{2}\right)& \Rightarrow \text{ Locus of }\left(x_1,y_1\right)\text{ is }\frac{2}{y^2}-\frac{1}{x^2}=1\end{array}$