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 3 , then the length of its latus rectum is:

Step-by-step solution

Given, difference of the lengths of major and minor axis is 10 . ⇒ 2 b - 2 a = 10 … (1) One of the focii is 0 ,   5 3 ⇒ b e = 5 3 … (2) Also a 2 = b 2 1 - e 2 .......(3) ⇒ a 2 = b 2 - 75 ⇒ b - a a + b = 75 ⇒ a + b = 15 … (4) From (1) and (4) a = 5 and b = 10 Hence length of the latus rectum = 2 a 2 b = 2 ⋅ 25 10 = 5