Embibe Experts Solutions for Chapter: Hyperbola, Exercise 1: AP EAPCET - 20 Aug 2021 Afternoon

The asymptotes of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, with any tangent to the hyperbola form a triangle whose area is $a^2\tan \left(\alpha \right)$. Then its eccentricity equals

If one focus of a hyperbola is $(3,0)$, the equation of its directrix is $4x-3y-3=0$ and its eccentricity $e=\frac{5}{4}$, then the co-ordinates of its vertex is

If the focal chord of the hyperbola subtends a right angle at the center, then its eccentricity is

The equation of the asymptotes of the hyperbola $2x^2+5xy+2y^2-11x-7y-4=0$ is

A hyperbola with centre at $(0,0)$ has its transverse axis along $X$-axis whose length is $12$. If $(8,2)$ is a point on the hyperbola, then its eccentricity is

If the eccentricity of a hyperbola is $\frac{5}{3},$ then the eccentricity of its conjugate hyperbola is