Let the length of the latus rectum of an ellipse with its major axis along x -axis and centre at the origin, be 8 . If the distance between the foci of this ellipse is equal to the length of its minor

Question

Let the length of the latus rectum of an ellipse with its major axis along x -axis and centre at the origin, be 8 . If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

TestHub · Accepted Answer

Let the ellipse be a 2 x 2 ​ + b 2 y 2 ​ = 1 Then, a 2 b 2 ​ = 8 , 2 a e − b 2 and b 2 = a 3 ( 1 − e 2 ) ⇒ a = 8 , b 2 = 32 Then, the equation of the ellipse 64 x 2 ​ + 32 y 2 ​ = 1 Hence, the point ( 4 3 ​ , 2 2 ​ ) lies on the ellipse.

Mathematics - Ellipse Question with Solution | TestHub

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