The centre of the ellipse$\frac{{{{(x + y - 2)}^2}}}{9} + \frac{{{{(x - y)}^2}}}{{16}} = 1$ is

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is $\pi\over2$, then the eccentricity of the ellipse is

The equation of an ellipse, whose vertices are $(2, -2), (2, 4)$ and eccentricity $\frac{1}{3}$, is

If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :

A ray of light through $(2,1)$ is reflected at a point $P$ on the $y$ - axis and then passes through the point $(5,3)$. If this reflected ray is the directrix of an ellipse with eccentrieity $\frac{1}{3}$ and the distance of the nearer focus from this directrix is $\frac{8}{\sqrt{53}}$, then the equation of the other directrix can be :

Let the ellipse $E : x ^2+9 y ^2=9$ intersect the positive $x$ - and $y$-axes at the points $A$ and $B$ respectively Let the major axis of $E$ be a diameter of the circle $C$. Let the line passing through $A$ and $B$ meet the circle $C$ at the point $P$. If the area of the triangle which vertices $A, P$ and the origin $O$ is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $m - n$ is equal to