G Tewani Solutions for Chapter: Hyperbola, Exercise 2: DPP

If a chord joining $P\left(a\sec \theta , a\tan \theta \right)$ and $Q\left(a\sec \alpha , a\tan \alpha \right)$ on the hyperbola $x^2-y^2=a^2$ is the normal at $P$, then $\tan \alpha$ is

The number of normal(s) of a rectangular hyperbola that can touch its conjugate is equal to

If the normal at a point $P$ to the hyperbola meets the transverse axis at $G$ and the value of $\frac{\mathrm{SG}}{\mathrm{SP}}$ is $6$, then the eccentricity of the hyperbola is (where $S$ is the focus of hyperbola)

If the normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ at any point $P\left(a\sec \theta ,b\tan \theta \right)$ meets the transverse and conjugate axes in $G$ and $g$, respectively, then value $PG$ is greater than 

If normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ drawn at an extremity of its latus rectum has slope equal to slope of line which meets hyperbola only once, then the eccentricity of hyperbola is

At the point of intersection of the rectangular hyperbola $xy=c^2$ and the parabola $y^2=4ax$, tangents to the rectangular hyperbola and the parabola make an angle $\theta$ and $\varphi$, respectively with the $x$-axis, then

Three points $A, B$ and $C$ are taken on a rectangular hyperbola $xy=4$, where $B$ and $C$ have co-ordinates $(-2, -2)$ and $\left(6, \frac{2}{3}\right)$ respectively and $A$ lies in the first quadrant. If the normal at $A$ is parallel to $BC$, then

A tangent is drawn at any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this tangent is intersected by the tangents at the vertices at points $P$ and $Q$, then which of the following is/are true? (Where $S, S^{\text{'}}$ are foci of hyperbola.)