For the hyperbola $\frac{{{x^2}}}{9} – \frac{{{y^2}}}{3} = 1$  the incorrect statement is :

If angle between asymptotes of hyperbola $\frac{{{x^2}}}{{{a^2}}} – \frac{{{y^2}}}{3} = 4$ is $\frac {\pi }{3}$ , then its conjugate hyperbola is

If the line $y = 2x + \lambda $ be a tangent to the hyperbola $36{x^2} – 25{y^2} = 3600$, then $\lambda = $

Consider the hyperbola

$\frac{x^2}{100}-\frac{y^2}{64}=1$

with foci at $S$ and $S_1$, where $S$ lies on the positive $x$-axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $\angle SPS _1=\alpha$, with $\alpha<\frac{\pi}{2}$. The straight line passing through the point $S$ and having the same slope as that of the tangent at $P$ to the hyperbola, intersects the straight line $S_1 P$ at $P_1$. Let $\delta$ be the distance of $P$ from the straight line $SP _1$, and $\beta= S _1 P$. Then the greatest integer less than or equal to $\frac{\beta \delta}{9} \sin \frac{\alpha}{2}$ is. . . . . . . 

A tangent to the hyperbola $\frac{{{x^2}}}{4} – \frac{{{y^2}}}{2} = 1$ meets $x-$ axis at $P$ and $y-$ axis at $Q$. Lines $PR$ and $QR$ are drawn such that $OPRQ$ is a rectangle (where $O$ is the origin). Then $R$ lies on