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