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

  • [JEE MAIN 2020]
  • A

    $e ^{2}+2 e -1=0$

  • B

    $e ^{2}+ e -1=0$

  • C

    $e ^{4}+2 e ^{2}-1=0$

  • D

    $e ^{4}+ e ^{2}-1=0$

Similar Questions

A tangent is drawn to the ellipse $\frac{{{x^2}}}{{32}} + \frac{{{y^2}}}{8} = 1$ from the point $A(8, 0)$ to touch the ellipse at point $P.$ If the normal at $P$ meets the major axis of ellipse at point $B,$ then the length $BC$ is equal to (where $C$ is centre of ellipse) - ............ $\mathrm{units}$

The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9 y^2=9$ meets its auxiliary circle at the point $M$. Then the area of the triangle with vertices at $A, M$ and the origin $O$ is

  • [IIT 2009]

For the ellipse $3{x^2} + 4{y^2} = 12$, the length of latus rectum is

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $(4,-1)$ and $(-2, 2)$ is

  • [JEE MAIN 2017]

Let $S = 0$ is an ellipse whose vartices are the extremities of minor axis of the ellipse $E:\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1,a > b$ If $S = 0$ passes through the foci of $E$ , then its eccentricity is (considering the eccentricity of $E$ as $e$ )