JEE PYQ: Ellipse Question 19
Question 19 - 2019 (08 Apr Shift 2)
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 $(0, 5\sqrt{3})$, then the length of its latus rectum is:
(a) 10 (b) 5 (c) 8 (d) 6
Show Answer
Answer: (b) 5
Solution
Focus at $(0, 5\sqrt{3}) \Rightarrow b > a$
$b^2e^2 = b^2 - a^2 = 75$, $b - a = 5$, $b + a = 15$
$b = 10$, $a = 5$
Latus rectum $= \frac{2a^2}{b} = \frac{50}{10} = 5$
BETA
