If the foci of an ellipse are $( \pm \sqrt 5 ,\,0)$ and its eccentricity is $\frac{{\sqrt 5 }}{3}$, then the equation of the ellipse is

  • A

    $9{x^2} + 4{y^2} = 36$

  • B

    $4{x^2} + 9{y^2} = 36$

  • C

    $36{x^2} + 9{y^2} = 4$

  • D

    $9{x^2} + 36{y^2} = 4$

Similar Questions

If the point of intersections of the ellipse $\frac{ x ^{2}}{16}+\frac{ y ^{2}}{ b ^{2}}=1$ and the circle $x ^{2}+ y ^{2}=4 b , b > 4$ lie on the curve $y^{2}=3 x^{2},$ then $b$ is equal to:

  • [JEE MAIN 2021]

Let $E_1: \frac{x^2}{9}+\frac{y^2}{4}=1$ be an ellipse. Ellipses $E_i$ 's are constructed such that their centres and eccentricities are same as that of $E _1$, and the length of minor axis of $E _{ i }$ is the length of major axis of $E _{ i +1}( i \geq 1)$. If $A _{ i }$ is the area of the ellipse $E _{ i }$, then $\frac{5}{\pi}\left(\sum_{ i =1}^{\infty} A _{ i }\right)$, is equal to _____

  • [JEE MAIN 2025]

On the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{8} = 1$ the point $M$ nearest to the line $2x - 3y + 25 = 0$ is

Minimum area of the triangle by any tangent to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ with the coordinate axes is

  • [IIT 2005]

The number of values of $c$ such that line $y = cx + c$, $c \in R$ touches the curve $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is