Mathematics - Application of Derivative Question with Solution | TestHub

The director circle of ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ is $x^2+y^2=3$ Let a point $\mathrm{P}(\sqrt{3}\cos \theta ,\sqrt{3}\sin \theta )$ Equation of chord of contact is x. $\sqrt{3}\cos \theta +2y\sqrt{3}\sin \theta -2=0$ It touches ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{r}}^2$

$$\begin{array}{rlr}& r=\frac{2}{\sqrt{3{\cos }^2\theta +12{\sin }^2\theta }}=\frac{2}{\sqrt{3+9{\sin }^2\theta }}& r_{\max }=\frac{2}{\sqrt{3}}\&r_{\min }=\frac{2}{\sqrt{12}}\Rightarrow \frac{A_{\max }}{A_{\min }}=4\end{array}$$