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Question

Question: The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. T...

The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is-

A

x2 + 2y2 = 100

B

x2 + 2y2\sqrt{2}y^{2} = 10

C

x2 – 2y2 = 100

D

None of these

Answer

x2 + 2y2 = 100

Explanation

Solution

2b2a=10\frac{2b^{2}}{a} = 10 and 2b = 2ae ̃ b = ae ̃ b2 = a2e2

̃ a2(1– e2) = a2e2 ̃ e = 12\frac{1}{\sqrt{2}}