In an ellipse, with centre at the origin, if the difference of the...

Given, difference of the lengths of major and minor axis is $10$.
$⇒ 2b - 2a = 10$ … (1)
One of the focii is \left(0, 5\sqrt{3}\right)$<br />$⇒ be = 5\sqrt{3}&hellip; (2)<br />Also{a}^{2} = {b}^{2}\left(1 - {e}^{2}\right) .......(3)
$⇒ {a}^{2} = {b}^{2} - 75$
$⇒ \left(b - a\right)\left(a + b\right) = 75$
$⇒ a + b = 15$ … (4)
From (1) and (4)
$a = 5 and b = 10$
Hence length of the latus rectum $= \dfrac{2{a}^{2}}{b} = 2 ⋅ \dfrac{25}{10} =5$