JEE PYQ: Ellipse Question 13
Question 13 - 2020 (07 Jan Shift 1)
If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:
(a) $\sqrt{3}$ (b) $3\sqrt{2}$ (c) $\frac{3}{\sqrt{2}}$ (d) $2\sqrt{3}$
Show Answer
Answer: (b) $3\sqrt{2}$
Solution
$2ae = 6 \Rightarrow ae = 3$, $\frac{2a}{e} = 12 \Rightarrow \frac{a}{e} = 6$
$a^2 = 18$, $b^2 = 18 - 9 = 9$
Latus rectum $= \frac{2b^2}{a} = \frac{18}{3\sqrt{2}} = 3\sqrt{2}$
BETA
