In an ellipse, with centre at origin, if difference of lengths of major axis and minor axis is 10 an

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10-2. Parabola, Ellipse, Hyperbola

hard

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

$6$

B

$5$

C

$8$

D

$10$

(JEE MAIN-2019)

Solution

$be = 5\sqrt 3 $

${b^2}{e^2} = 75$

$\left( {b – a} \right)\left( {b + a} \right) = 75 \Rightarrow b + a = 15$

$ \Rightarrow b = 10,a = 5$

$LR = \frac{{2{a^2}}}{b}5$

Standard 11

Mathematics

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