The equation of a line passing through the centre of a rectangular hyperbola is $x -y -1 = 0$. If one of the asymptotes is $3x -4y -6 = 0$, the equation of other asymptote is

Let $\mathrm{A}\,(\sec \theta, 2 \tan \theta)$ and $\mathrm{B}\,(\sec \phi, 2 \tan \phi)$, where $\theta+\phi=\pi / 2$, be two points on the hyperbola $2 \mathrm{x}^{2}-\mathrm{y}^{2}=2$. If $(\alpha, \beta)$ is the point of the intersection of the normals to the hyperbola at $\mathrm{A}$ and $\mathrm{B}$, then $(2 \beta)^{2}$ is equal to ..... .

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

The length of the latus rectum of the hyperbola $25x^2 -16y^2 = 400$ is -

If $e$ and $e’$ are eccentricities of hyperbola and its conjugate respectively, then

$P(6, 3)$ is a point on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ . If the normal at point $P$ intersect the $x-$ axis at $(10, 0)$ , then the eccentricity of the hyperbola is