If the latus rectum through one focus subtends a right angle at the farther vertex of the hyperbola then its eccentricity is

Explanation

Let the equation of Hyperbola `x^2/a^2− y^2/b^2=1`

The Latus Rectum `LL′` is substending `90^o` at `A′`
. So, the lines `A′L, A′L′` and `LL′` are sides of right angled triangle.

So, we can apply Pythagoras Theorem to it.

where `LL′`= `2b^2/a`=Length of `LR`

`A′L=(ae+a)^2+(b^2/a−0)^2`

`A′L′=A′L`(due to symmetry about X-axis)

So, by Pythagoras Theorem,
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