Question

$S_1,S_2$ are foci of an ellipse of major axis of length $10$ units and $P$ is any point on the ellipse such that perimeter of triangle $P{S}_1{S}_2$ is $15$. Then eccentricity of the ellipse is:

• A. $0.5$
• B. $0.25$
• C. $0.28$
• D. $0.75$

Answer 1

The correct option is A $0.5$

If $a>b$, then length of major axis $=10$

$\Rightarrow a=5$

Perimeter of $△P{S}_1{S}_2$ is $15$

$\Rightarrow 2a+2ae=15$

$\Rightarrow 10+10e=15$

$e=0.5$