An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ and the parabola $x^2=4(y+b)$ are such that the two foci of the ellipse and the end points of the latusrectum of parabola are the vertices of a square. The eccentricity of the ellipse is
An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ and the parabola $x^2=4(y+b)$ are such that the two foci of the ellipse and the end points of the latusrectum of parabola are the vertices of a square. The eccentricity of the ellipse is
- [KVPY 2017]
- A
$\frac{1}{\sqrt{13}}$
- B
$\frac{2}{\sqrt{13}}$
- C
$\frac{1}{\sqrt{11}}$
- D
$-\frac{2}{\sqrt{11}}$
Similar Questions
If $y = mx + c$ is tangent on the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$, then the value of $c$ is
If $y = mx + c$ is tangent on the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$, then the value of $c$ is
The length of the axes of the conic $9{x^2} + 4{y^2} - 6x + 4y + 1 = 0$, are
The length of the axes of the conic $9{x^2} + 4{y^2} - 6x + 4y + 1 = 0$, are
Find the equation of the ellipse, with major axis along the $x-$ axis and passing through the points $(4,\,3)$ and $(-1,\,4)$
Find the equation of the ellipse, with major axis along the $x-$ axis and passing through the points $(4,\,3)$ and $(-1,\,4)$
The locus of mid-points of the line segments joining $(-3,-5)$ and the points on the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ is :
The locus of mid-points of the line segments joining $(-3,-5)$ and the points on the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$ is :
- [JEE MAIN 2021]
Extremities of the latera recta of the ellipses $\frac{{{x^2}}}{{{a^2}}}\,\, + \,\,\frac{{{y^2}}}{{{b^2}}}\, = \,1\,$ $(a > b)$ having a given major axis $2a$ lies on
Extremities of the latera recta of the ellipses $\frac{{{x^2}}}{{{a^2}}}\,\, + \,\,\frac{{{y^2}}}{{{b^2}}}\, = \,1\,$ $(a > b)$ having a given major axis $2a$ lies on