Dr. SK Goyal Solutions for Chapter: Hyperbola, Exercise 3: INTRODUCTORY EXERCISE 7.3

Tangents drawn from a point on the circle $x^2+y^2=9$ to the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$, then tangents are at angle :

If $H\equiv \frac{x^2}{a^2}-\frac{y^2}{b^2}-1=0,C\equiv \frac{x^2}{a^2}-\frac{y^2}{b^2}+1=0$ and $A\equiv \frac{x^2}{a^2}-\frac{y^2}{b^2}=0$ then $H,A$ and $C$ are in :

The angle between the asymptotes of $\frac{x^2}{4}-\frac{y^2}{9}=1$ is equal to :

If $e$ and $e_1$ are the eccentricities of the hyperbolas $xy=c^2$ and $x^2-y^2=a^2$, then ${\left(e+e_1\right)}^2$ is equal to :

A ray emanating from the point $(-\sqrt{41},0)$ is incident on the hyperbola $16x^2-25y^2=400$ at the point $P$ with abscissa $10$ . Then the equation of the reflected ray after first reflection and point $P$ lies in second quadrant is :

The equations of the transverse and conjugate axes of a hyperbola are respectively $x+2y-3=0, 2x-y+4=0,$ and their respective lengths are $\sqrt{2}$ and $\frac{2}{\sqrt{3}}.$ The equation of the hyperbola is

Find the equation of that diameter which bisects the chord $7x+y-2=0$ of the hyperbola $\frac{x^2}{3}-\frac{y^2}{7}=1$.

A circle cuts the rectangular hyperbola $xy=1$ in points $\left(x_r,y_r\right),r=1,2,3,4$ then prove that
$x_1{x}_2{x}_3{x}_4=y_1{y}_2{y}_3{y}_4=1.$