Eccentricity of conjugate hyperbola of $16x^2 - 9y^2 - 32x - 36y - 164 = 0$ will be-
$\frac{5}{3}$
$\frac{5}{4}$
$\frac{12}{5}$
$\frac{13}{12}$
If the circle $x^2 + y^2 = a^2$ intersects the hyperbola $xy = c^2 $ in four points $ P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4), $ then
Locus of mid points of chords of hyperbola $x^2 -y^2 = a^2$ which are tangents to the parabola $x^2 = 4by$ will be -
The length of the transverse axis of a hyperbola is $7$ and it passes through the point $(5, -2)$. The equation of the hyperbola is
The normal to the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1$ at the point $(8,3 \sqrt{3})$ on it passes through the point
Find the coordinates of the foci and the vertices, the eccentricity,the length of the latus rectum of the hyperbolas : $\frac{x^{2}}{9}-\frac{y^{2}}{16}=1.$