The centre of the hyperbola $9x^2 - 16y^2 + 18x + 32y - 151 = 0$ is

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be $2a$ and $2b$,respectively,and one focus and the corresponding directrix of this hyperbola be $(-5, 0)$ and $5x + 9 = 0$,respectively. If the product of the focal distances of a point $(\alpha, 2\sqrt{5})$ on the hyperbola is $p$,then $4p$ is equal to . . . . . . .

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

The equation of the normal to the hyperbola $\frac{x^2}{16} - \frac{y^2}{9} = 1$ at $(-4, 0)$ is

The tangents drawn to the hyperbola $5x^2 - 9y^2 = 90$ through a variable point $P$ make the angles $\alpha$ and $\beta$ with its transverse axis. If $\alpha$ and $\beta$ are complementary angles,then the locus of $P$ is

The descending order of magnitude of the eccentricities of the following hyperbolas is:
$A$. $A$ hyperbola whose distance between foci is three times the distance between its directrices.
$B$. Hyperbola in which the transverse axis is twice the conjugate axis.
$C$. Hyperbola with asymptotes $x+y+1=0$ and $x-y+3=0$.