The difference of the focal distance of any point on the hyperbola $9{x^2} - 16{y^2} = 144$, is

 A hyperbola passes through the point $P\left( {\sqrt 2 ,\sqrt 3 } \right)$ has foci at $\left( { \pm 2,0} \right)$. Then the tangent to this hyperbola at  $P$ also passes through the point

The equation of the tangent parallel to $y - x + 5 = 0$ drawn to $\frac{{{x^2}}}{3} - \frac{{{y^2}}}{2} = 1$ is

For the Hyperbola ${x^2}{\sec ^2}\theta - {y^2}cose{c^2}\theta = 1$ which of the following remains constant when $\theta $ varies $= ?$

The eccentricity of the hyperbola conjugate to ${x^2} - 3{y^2} = 2x + 8$ is

Area of the quadrilateral formed with the foci of the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ and $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} =  - 1$ is