Dr. SK Goyal Solutions for Chapter: Ellipse, Exercise 6: Multiple Choice I

If $O$ is the centre, $OA$ the semi-major axis and $S$ the focus of an ellipse, the eccentric angle of any point $P$ is :

Let $P$ be a variable point on the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ with foci at $S$ and $S^{\text{'}}$. If $A$ be the area of triangle $PS{S}^{\text{'}}$, then the maximum value of $A$ is :

If one end of a diameter of the ellipse $4x^2+y^2=16$ is $\left(\sqrt{3},2\right)$, then the other end is:

For the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, the equation of the diameter conjugate to $ax-by=0$ is :

If the polar with respect to $y^2=4ax$ touches the ellipse $\frac{x^2}{{\mathrm{\alpha }}^2}+\frac{y^2}{{\mathrm{\beta }}^2}=1,$ the locus of its pole is

$P$ is a variable point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=2$ whose foci are $F_1$ and $F_2$. The maximum area of $∆P{F}_1{F}_2$ is :

The locus of $P$ satisfying the condition $\left|P{F}_1\right|+\left|P{F}_2\right|=10;F_1\equiv \left(1,2\right);F_2\equiv \left(12,2\right)$ is :

If $CF$ is the perpendicular from the centre $C$ of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ on the tangent at any point $P$ and $G$ is the point when the normal at $P$ meets the major axis, then $CF·PG=$