Question

$PS{P}^{\prime }$ is focal chord of the ellipse $4x^2+9y^2=36$. lf $SP=4$ then $S{P}^{\prime }$ :
(Note : $S$ is a focus and $P$ and $P^{\prime }$ are points on the ellipse)

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{4}{3}$
• D. $\frac{4}{5}$

Answer 1

Answer: (D)

$\frac{4}{5}$

Given equation of ellipse is

$4x^2+9y^2=36$

$\frac{x^2}{9}+\frac{y^2}{4}=1$

Here , $a=3,b=2$

We have $\frac{1}{PS}+\frac{1}{P{S}^{\prime }}=\frac{2a}{b^2}$

$\Rightarrow \frac{P{S}^{\prime }+4}{4.P{S}^{\prime }}=\frac{3}{2}$

$\Rightarrow P{S}^{\prime }=\frac{4}{5}$