The length of the latus rectum of $9x^2 + 25y^2 - 90x - 150y + 225 = 0$ is

If the origin is the centre,the $X$-axis is the major axis,and $\sqrt{\frac{2}{5}}$ is the eccentricity of an ellipse which passes through $(-3, 1)$,then the equation of that ellipse is:

Let $P$ be a variable point on the ellipse $x^2 + 3y^2 = 3$. Then the maximum perpendicular distance of $P$ from the line $x - y = 10$ is (in $\sqrt{2}$)

If the line $x \cos \alpha + y \sin \alpha = 2 \sqrt{3}$ is a tangent to the ellipse $\frac{x^2}{16} + \frac{y^2}{8} = 1$ and $\alpha$ is an acute angle,then $\alpha = $

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

If the latus rectum of an ellipse subtends a right angle at the centre of that ellipse,then the eccentricity of that ellipse is