Embibe Experts Solutions for Chapter: Ellipse, Exercise 1: BITSAT 2019

The locus of the foot of perpendicular drawn from the centre of the ellipse $x^2+3y^2=6$ on any tangent to it is

The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9y^2=9$ meets its auxiliary circle at the point $M$. Then, the area of the triangle with vertices at $A, M$ and the origin $O$ is

If the length of the major axis of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is three times the length of minor axis, its eccentricity is

If $p$ and $p^{\text{'}}$ denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length $a$, respectively, on a tangent to the ellipse and $r$ denotes the focal distance of the point, then