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JEE Main201911 Jan 2019Evening ShiftMathematicsEllipseActual

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?

Options

  1. A(4 2 , 2 2 )
  2. B(4 3 , 2 2 )
  3. C(4 3 , 2 3 )
  4. D(4 2 , 2 3 )

Correct answer

B. (4 3 , 2 2 )

Step-by-step solution

Let the ellipse be x² a² + y² b² =1 Then, 2 b² a =8,2 a e-b² and b²=a³ (1-e² ) a=8, b²=32 Then, the equation of the ellipse x² 64 + y² 32 =1 Hence, the point (4 3 , 2 2 ) lies on the ellipse.

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