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

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

Equation of the hyperbola with eccentricity $\frac{3}{2}$ and foci at $\left(\pm 2,0\right)$ is $5x^2-4y^2=k^2$. What is the value of $k$ $?$

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

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

The equation of tangents to the hyperbola $3x^2-2y^2=6$, which is perpendicular to the line $x-3y=3$, are

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

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 $\left(8,3\sqrt{3}\right)$?

The equation of the tangent to the curve $4x^2-9y^2=1$ which is parallel to $4y=5x+7$ is