Mathematics - Ellipse Question with Solution | TestHub

$\mathrm{PS}+{\mathrm{PS}}^{\prime }=2\times 3\sqrt{2}$
${\mathrm{b}}^2={\mathrm{a}}^2\left(1-{\mathrm{e}}^2\right)\Rightarrow 9=18\left(1-{\mathrm{e}}^2\right)$
$\Rightarrow \mathrm{e}=\frac{1}{\sqrt{2}}$
Directrix $\mathrm{x}=\frac{\mathrm{a}}{\mathrm{e}}=\frac{3\sqrt{2}}{\frac{1}{\sqrt{2}}}=6$
$PS\cdot P{S}^{\prime }=\left|\frac{1}{\sqrt{2}}(3\sqrt{2}\cos \theta -6)\frac{1}{\sqrt{2}}(3\sqrt{2}\cos \theta +6)\right|$
$=\frac{1}{2}\left|18{\cos }^2\theta -36\right|$
${\left(\mathrm{PS}\cdot {\mathrm{PS}}^{\prime }\right)}_{\max }=18;(\mathrm{PS}\cdot \mathrm{PS}{)}_{\min }=9$
sum $=27$