JEE Main20206 Sep 2020Evening ShiftMathematicsEllipseActual

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :

Options

Ae 4 + 2 e 2 - 1 = 0
Be 2 + e - 1 = 0
Ce 4 + e 2 - 1 = 0
De 2 + 2 e - 1 = 0

Correct answer

C. e 4 + e 2 - 1 = 0

Step-by-step solution

Equation of normal at a e , b 2 a a 2 x a e - b 2 y b 2 / a = a 2 - b 2 it passes through ( 0 , - b ) a b = a 2 e 2 a 2 b 2 = a 4 e 4                 ∵ b 2 = a 2 ( 1 - e 2 1 - e 2 = e 4

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