The length of the transverse axis of the hyperbola $3x^2 - 4y^2 = 32$ is

If the length of the transverse and conjugate axes of a hyperbola are $8$ and $6$ respectively,then the difference of the focal distances of any point on the hyperbola will be

The foci of the hyperbola $4x^2 - 9y^2 - 36 = 0$ are:

The eccentricity of the curve $x^2 - y^2 = 1$ is

$A$ tangent to a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ intercepts a length of unity from each of the coordinate axes. Then the point $(a, b)$ lies on the rectangular hyperbola:

The tangent to the hyperbola $xy = c^2$ at the point $P(ct, c/t)$ intersects the $x$-axis at $T$ and the $y$-axis at $T'$. The normal to the hyperbola at $P$ intersects the $x$-axis at $N$ and the $y$-axis at $N'$. If the areas of the triangles $PNT$ and $PN'T'$ are $\Delta$ and $\Delta'$ respectively,then $\frac{1}{\Delta} + \frac{1}{\Delta'}$ is: