If the eccentricity of an ellipse is $5/8$ and the distance between its foci is $10$,then its latus rectum is

The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9y^2=9$ meets its auxiliary circle at the point $M$. Then the area of the triangle with vertices at $A$,$M$,and the origin $O$ is

If the distance between the directrices of an ellipse is three times the distance between its foci,then the eccentricity of the ellipse is:

The equation of the normal to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ at the point $(a \cos \theta, b \sin \theta)$ is

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

If the focal distance of an endpoint of the minor axis of an ellipse (taking its axes as the $x$ and $y$ axes respectively) is $k$ and the distance between its foci is $2h$,then its equation is: