Embibe Experts Solutions for Chapter: Hyperbola, Exercise 2: Exercise-2

The sides $AC$ and $AB$ of a triangle $ABC$ touch the conjugate hyperbola of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{{ b}^2}=1$ at $C$ and $B$ respectively. If the vertex $A$ lies on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{{ b}^2}=1$, the side $BC$

If $AB$ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that $OAB$ ($O$ is the origin) is an equilateral triangle, then the eccentricity $\text{'}e\text{'}$ of the hyperbola satisfies:

The length of that focal chord of the hyperbola $xy=8$ which touches the circle $x^2+y^2=8$ is.

The sum of lengths of perpendiculars drawn from focii to any real tangent to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ is always greater than $a$, then find maximum value of $a$.

Let $x^2+y^2=r^2$ and $xy=1$ intersect at $A\&B$ in first quadrant, If $AB=\sqrt{14}$ then find the value of $r$.

Which of the following equations in parametric form can represent a hyperbolic profile, where $\text{'}t\text{'}$ is a parameter.

If two distinct tangents can be drawn from the point $(\alpha ,2)$ on different branches of the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$, then the range of $\alpha$ is subset of

A rectangular hyperbola whose centre is $C$ is cut by any circle of radius $r$ in four points $P, Q, R$ and $S$. Then $C{P}^2+C{Q}^2+C{R}^2+C{S}^2=$