Embibe Experts Solutions for Chapter: Ellipse, Exercise 3: Level 3

If $S$ and $S^{\text{'}}$ are the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1,$ and $P$ is any point on it, then range of values of $SP·S^{\text{'}}P$ is

Let $P_i$ and ${P_i}^{\text{'}}$ be the feet of the perpendiculars drawn from foci $S,$ $S^{\text{'}}$ on a tangent $T_i$ to an ellipse whose length of semi-major axis is $20,$ if $\sum _{i=1}^{10}\left(S{P}_i\right)\left(S^{\text{'}}{P}_i^{\text{'}}\right)=2560,$ then the value of eccentricity is

The eccentricity of the curve represented by the equation $x^2+2y^2-2x+3y+2=0$ is

Tangents are drawn to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\left(a>b\right)$ and the circle $x^2+y^2=a^2$ at the points where a common ordinate cuts them (on the same side of the $x$ -axis). Then the greatest acute angle between these tangents is given by

The locus of point of intersection of two tangents of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, meeting at right angles is

At a point $P$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ tangent $PQ$ is drawn. If the point $Q$ be at a distance $\frac{1}{p}$ from the point $P$, where $‘p’$ is distance of the tangent from the origin, then the locus of the point $Q$ is

If the normal at any point $P$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the auxiliary circle at $Q$ and $R$, such that $\angle QOR=90°$, where $O$ is the center of the ellipse, then

If the normal at any point $P$ of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ meets the coordinate axes at$M$ and $N$, respectively, then $PM:PN$ equals to