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:

Question

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:, 6, 10, 8, 5

MARKS App · Accepted Answer

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

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