G Tewani Solutions for Chapter: Ellipse, Exercise 1: DPP

A point $P$ moves on $xy-$plane such that $PS+P{S}^{\text{'}}=4$, where $S(K, 0)$ and $S^{\text{'}}(-K, 0),$ then which of the following is not true about the locus of $P ?$

The ratio of the area enclosed by the locus of the midpoint of $PS$ and area of the ellipse is ($P$ be any point on the ellipse and $S$ is its focus)

Number of integral values of $\alpha$ for which the point $\left(7-\frac{5}{4}\alpha , \alpha \right)$ lies inside the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is

Coordinates of the vertices $B$ and $C$ of a triangle $ABC$ are $\left(2,0\right)$ and $\left(8,0\right)$, respectively. The vertex $A$ is varying in such a way that $4\tan \frac{B}{2}·\tan \frac{C}{2}=1.$ Then locus of $A$ is

$PQ$ and $QR$ are two focal chords of an ellipse and the eccentric angles of $P, Q$ and $R$ are $2\alpha ,2\beta$ and $2\gamma$ respectively, then $\tan \beta \tan \gamma$ is

In triangle $ABC, a=4$ and $b=c= 2\sqrt{2}$. A point $P$ moves within the triangle such that the square of its distance from $BC$ is half the area of rectangle contained by its distances from the other two sides. If $D$ is the centre of locus of $P$, then

Extremities of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\left(a>b\right)$ having a major axis $2a$ lies on:

Identify correct statement(s) about conic $\sqrt{{\left(x-5\right)}^2+{\left(y-7\right)}^2}+\sqrt{{\left(x+1\right)}^2+{\left(y+1\right)}^2}=12$