Mathematics - Ellipse Question with Solution | TestHub

Ellipse equation is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, Area $=\pi ab$ Let $P=(a\cos \theta ,b\sin \theta )$ $S=(ae,0)$ M(h,k) mid point of PS $\Rightarrow h=\frac{ae+a\cos \theta }{2};k=\frac{b\sin \theta }{2}$ $=\frac{h-\frac{ae}{2}}{a/2}+\frac{k^2}{\left(b^2/4\right)}=1$, locus of $(\mathrm{h},\mathrm{k})$ is ellipse Area $=\pi \left(\frac{a}{2}\right)\left(\frac{b}{2}\right)=\frac{1}{4}\pi ab$