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

The curve $xy=c\left(c>0\right)$ and the circle $x^2+y^2=25$ touch at two points, then distance between the points of contact is

If the tangent on the point $\left(3\sec \varphi ,4\tan \varphi \right)$ (which is in first quadrant) of the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ is perpendicular to $3x+8y-12=0$, then the value of $\varphi$ is (in degree).

The line $y=x$ intersects the hyperbola $\frac{x^2}{9}-\frac{y^2}{25}=1$ at the points $P$ and $Q$. Then find eccentricity of ellipse with $PQ$ as major axis and miror axis of length $\frac{5}{\sqrt{2}}$.

With respect to the hyperbola $(3x-3y{)}^2-(2x+2y{)}^2=36$

For hyperbola represented by$16x^2-3y^2-32x+12y-44=0$, which of the following statement is INCORRECT

Find the equation of latus rectum of rectangular hyperbola $xy=c^2$

The number of points from where a pair of perpendicular tangents can be drawn to the hyperbola,$x^2{\sec }^2\alpha -y^2{cosec}^2\alpha =1,\alpha \in (0,\pi /4)$, is :

Equation of common tangent to ellipse $5x^2+2y^2=10$, and hyperbola $11x^2-3y^2=33$ is