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

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

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

$P$ is the extremity of the latusrectum of ellipse $3x^2+4y^2=48$ in the first quadrant. The eccentric angle of $P$ is

Let $P$ be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and the line through $P$ parallel to the $Y$ -axis meets the circle $x^2+y^2=9$ at $Q,$ where $P, Q$ are on the same side of the $X$ -axis. If $R$ is a point on $PQ$ such that $\frac{PR}{RQ}=\frac{1}{2},$ then the locus of $R$ is

Consider a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ at any point. The locus of the mid-point of the portion intercepted between the axes is

Consider the curve $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of