Embibe Experts Solutions for Chapter: Hyperbola, Exercise 1: WBJEE 2020

A double ordinate $PQ$ of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is such that $\Delta OPQ$ is equilateral $O$ being the centre of the hyperbola. Then the eccentricity $e$ satisfies the relation

For the hyperbola $\frac{x^2}{{\cos }^2\alpha }-\frac{y^2}{{\sin }^2\alpha }=1,$ which of the following remains fixed when $\alpha$ varies?

The equation of the directrices of the hyperbola $3x^2-3y^2-18x+12y+2=0$ is

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity $e$ is

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+9y^2=9,$ then the ratio $a^2:b^2$ equals

A hyperbola, having the transverse axis of length $2\sin \theta$ is confocal with the ellipse $3x^2+4y^2=12.$ Its equation is

Let $P(4, 3)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ If the normal at $P$ intersects the $X-$axis at $(16, 0),$ then the eccentricity of the hyperbola is

Equation of a tangent to the hyperbola $5x^2-y^2=5$ and which passes through an external point $(2, 8)$ is