Question

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at $\left(0,5\sqrt{3}\right),$ then the length of its latus rectum is:

• A. $10$
• B. $8$
• C. $5$
• D. $6$

Answer 1

Answer: (C)

Let equation of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$2a-2b=10\dots \left(1\right)$
$ae=5\sqrt{3}\dots \left(2\right)$
$\frac{2b^2}{a}=?$
$b^2=a^2\left(1-e^2\right)$
$b^2=a^2-a^2{e}^2$
$b^2=a^2-25\times 3$
$\Rightarrow b=5$ and $a=10$
$\therefore$ length of L.R. $=\frac{2\left(25\right)}{10}=5$