Embibe Experts Solutions for Chapter: Hyperbola, Exercise 3: Exercise-3

An ellipse intersects the hyperbola $2x^2-2y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellipse $x^2+4y^2=4.$ If the hyperbola passes through a focus of the ellipse, then

Let $P(6,3)$ be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ If the normal at the point $P$ intersects the $X$ -axis at $(9,0),$ then the eccentricity of the hyperbola is

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1$. The points of contact of the tangents on the hyperbola are

The equation of the hyperbola, whose foci are $\left(-2,0\right)$ and $\left(2,0\right)$ and eccentricity is $2$, is given by