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, ), then the length of its latus rectum is

Engineering

Mathematics

Standard Ellipse

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, $5 \sqrt{3}$ ), then the length of its latus rectum is

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$be = 5 \sqrt{3}$

b²e² = 75

(b – a) (b + a) = 75 ⇒ b + a = 15

⇒ b = 10, a = 5

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