Question

A point $P$ on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ has the eccentric angle $\frac{\pi }{8}$. The sum of the distance of $P$ from the two foci is

• A. $5$
• B. $6$
• C. $10$
• D. $3$

Answer 1

The correct option is C $10$

Given,ellipse equation as $\frac{x^2}{25}+\frac{y^2}{9}=1$
Length of major axis, $a=5$ and length of minor axis, $b=3$
$P$ is a point on the ellipse whose eccentricity is $\frac{\pi }{8}.$
We know that, sum of the distances of any point on the ellipse from its foci equal to twice the major axis.
Let $S,S^{\prime }$ be foci of ellipse and $a,b$ as the length of major,minor axis respectively.
$\Rightarrow SP+S^{\prime }P=2a$
$\Rightarrow SP+S^{\prime }P=2\times 5=10$