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

The eccentricity of the hyperbola with latus rectum $12$ and semi-conjugate axis $2\sqrt{3}$, is

If the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide, then the value of $b^2$ is

If $e$ and $e^{\text{'}}$ be the eccentricities of a hyperbola and its conjugate, then $\frac{1}{e^2}+\frac{1}{e{\text{'}}^2}$ is equal to

The foci of the hyperbola $4x^2-9y^2-1=0$ are

The hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passes through the point $\left(3\sqrt{5},1\right)$ and the length of its latus rectum is $\frac{4}{3}$ units. The length of the conjugate axis is

The eccentricity of the hyperbola $16x^2-9y^2=1$ is

Which one of the following points does not lie on the normal to the hyperbola, $\frac{x^2}{16}-\frac{y^2}{9}=1$ drawn at the point $\left(8,3\sqrt{3}\right)$?

Consider a hyperbola $H : x^2-2y^2=4$. Let the tangent at a point $P(4,\sqrt{6})$ meet the $x$-axis at $Q$ and latus rectum at $R\left(x_1,y_1\right),x_1>0$. If $F$ is a focus of $H$ which is nearer to the point $P$, then the area of $\Delta QFR$ (in sq. units) is equal to