If $B$ and $B^{\prime}$ are the ends of the minor axis and $S$ and $S^{\prime}$ are the foci of the ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$, then the area of the rhombus $SBS^{\prime}B^{\prime}$ will be

The center of the ellipse $x^2+2y^2-4x+12y+14=0$ is

Consider the parabola $P : y^2 = 4x$ and the ellipse $E : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Let the line segment joining the points of intersection of $P$ and $E$ be their common latus rectum. If the eccentricity of $E$ is $e$, then $e^2 + 2\sqrt{2}$ is equal to . . . . . .

If the normal drawn at the point $(2, -1)$ to the ellipse $x^2 + 4y^2 = 8$ meets the ellipse again at $(a, b)$,then $17a =$

If the line $x \cos \alpha + y \sin \alpha = p$ is normal to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then

Let $E$ be the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$. For any three distinct points $P, Q$ and $Q^{\prime}$ on $E$,let $M(P, Q)$ be the mid-point of the line segment joining $P$ and $Q$,and $M(P, Q^{\prime})$ be the mid-point of the line segment joining $P$ and $Q^{\prime}$. Then the maximum possible value of the distance between $M(P, Q)$ and $M(P, Q^{\prime})$,as $P, Q$ and $Q^{\prime}$ vary on $E$,is: