Question

If $S$ and $S^{'}$ are the foci of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{16}=1$ and if $P S P^{'}$ is a focal chord with $S P=8$, then $S S^{\prime}$ is equal to

• A. $4+S^{'} P$
• B. $S^{'} P-1$
• C. $4+S P$
• D. $S P-1$

Answer 1

Answer: (A)

Given equation of ellipse
$\frac{x^{2}}{25}+\frac{y^{2}}{16}=1 $
Here, $a=5 $ and $b=4 $
$e =\sqrt{1-\frac{b^{2}}{a^{2}}}=\sqrt{1-\frac{16}{25}} $
$=\sqrt{\frac{9}{25}}=\frac{3}{5}$

Also,$P S+P S^{'}=2 a=2 \times 5=10 $
$ \Rightarrow P S^{'}=10-8 \,\,\,{[\because S P=8]} $
$\Rightarrow P S^{'}=2 $
Now, $S S^{'}=2 a e=2 \times 5 \times \frac{3}{5}=6$
From options, $ S S^{'}=4+S^{'} P$