Embibe Experts Solutions for Exercise 1: Andhra Pradesh Board-2020

Find the equation of the ellipse in the standard form whose distance between foci is $2$ and length of latus rectum is $\frac{15}{2}$.

If a tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 (a>b)$ meets its major axis and minor axis at $M$ and $N$ respectively, then prove that $\frac{a^2}{(CM{)}^2}+\frac{b^2}{(CN{)}^2}=1$, where $C$ is the centre of the ellipse.

Find the equation of the ellipse referred to its major and minor axes as the co-ordinate axes $x, y$ respectively with latus rectum of length $4$ and distance between foci $4\sqrt{2}$.

Find the equation of tangents to the ellipse $2x^2+y^2=8$ which is parallel to $x-2y+4=0$.

Find the equation of tangents to the ellipse $2x^2+y^2=8$ which is perpendicular to $x+y+2=0$

$S$ and $T$ are the foci of an ellipse and $B$ is one end of the minor axis. If $STB$ is an equilateral triangle, then find the eccentricity of the ellipse.

Find the condition for the line $x\cos \alpha +y\sin \alpha =p$ to be a tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.