If the foci and vertices of an ellipse be $( \pm 1,\;0)$ and $( \pm 2,\;0)$, then the minor axis of the ellipse is

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is

In the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, the equation of diameter conjugate to the diameter $y = \frac{b}{a}x$, is

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

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

Let $P$ is any point on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ . $S_1$ and $S_2$ its foci then maximum area of $\Delta PS_1S_2$ is (in square units)