The equation of the ellipse whose foci are $(\pm 5, 0)$ and one of its directrices is $5x = 36$ is:

Find the equation for the ellipse that satisfies the given conditions: Major axis on the $x-$ axis and passes through the points $(4, 3)$ and $(6, 2)$.

An ellipse has $OB$ as semi-minor axis,$S$ and $S^{\prime}$ are foci and angle $\angle SBS^{\prime}$ is a right angle. Then the eccentricity of the ellipse is

At which points on the ellipse $4x^2 + 9y^2 = 1$ is the tangent line parallel to the line $8x = 9y$?

If the chord through the points whose eccentric angles are $\theta$ and $\phi$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ passes through the focus,then the value of $(1 + e) \tan(\frac{\theta}{2}) \tan(\frac{\phi}{2})$ is

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$.