If $e$ and $e'$ are the eccentricities of a hyperbola and its conjugate hyperbola respectively,then $\frac{1}{e^2} + \frac{1}{e'^2} = \dots$

If the vertices of a hyperbola are at $(-2, 0)$ and $(2, 0)$ and one of its foci is at $(-3, 0)$,then which one of the following points does not lie on this hyperbola?

The locus of the point of intersection of the lines $bxt - ayt = ab$ and $bx + ay = abt$ is

Given the points $A(0,4)$ and $B(0, -4)$. Then the equation of the locus of the point $P(x,y)$ such that $|AP - BP| = 6$,is

The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is

Find the equation of the hyperbola with eccentricity $e = 3/2$ and foci at $(\pm 2, 0)$.