The eccentricity of the hyperbola $2{x^2} - {y^2} = 6$ is

Foci of the hyperbola $\frac{{{x^2}}}{{16}} - \frac{{{{(y - 2)}^2}}}{9} = 1$ are

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $\frac{y^{2}}{9}-\frac{x^{2}}{27}=1$

Let a line $L: 2 x+y=k, k\,>\,0$ be a tangent to the hyperbola $x^{2}-y^{2}=3 .$ If $L$ is also a tangent to the parabola $y^{2}=\alpha x$, then $\alpha$ is equal to :

Let the eccentricity of the hyperbola $H : \frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1$ be $\sqrt{\frac{5}{2}}$ and length of its latus rectum be $6 \sqrt{2}$, If $y =2 x + c$ is a tangent to the hyperbola $H$, then the value of $c ^{2}$ is equal to

The combined equation of the asymptotes of the hyperbola $2{x^2} + 5xy + 2{y^2} + 4x + 5y = 0$