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

The equations of the directrices of the ellipse $9x^2 + 4y^2 - 18x - 16y - 11 = 0$ are

If the normal at an end of a latus rectum of an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ passes through an extremity of the minor axis,then the eccentricity $e$ of the ellipse satisfies:

Let $P$ and $Q$ be the foci of an ellipse and let $R$ be one end of its minor axis. If $\triangle PQR$ is an equilateral triangle,then the eccentricity of the ellipse is equal to

Find the locus of the midpoint of the portion of the tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ intercepted between the axes.

The tangent to the ellipse $9x^2 + 16y^2 = 288$ making equal intercepts on the co-ordinate axes intersects the $X$-axis and the $Y$-axis in the points $A$ and $B$ respectively. Then $\text{Area}(\triangle OAB) = $ (where $O$ is origin)