If an ellipse with foci at $(3,3)$ and $(-4,4)$ is passing through the origin, then the eccentricity of that ellipse is

If $m$ is the length of the latusrectum and $n$ is the length of the major-axis of the ellipse $25 x^2+16 y^2-150 x-64 y-111=0$, then the ordered pair $(m, n)=$

If $P(\theta)$ and $Q\left(\frac{\pi}{2}+\theta\right)$ are two points on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the locus of mid-point of $P Q$ is $\frac{x^2}{\alpha^2}+\frac{y^2}{\beta^2}=1$, then $\frac{a+b}{\alpha+\beta}=$

The length of the latusrectum of an ellipse is 6 units and the distance between a focus and its nearest vertex on the major-axis is $5 / 3$ units. If $e$ is the eccentricity of this ellipse, then $e$ satisfies the equation