The eccentricity of the hyperbola $4x^2 - 9y^2 = 36$ is

The equation of the line passing through the points $\left(ct_1, \frac{c}{t_1}\right)$ and $\left(ct_2, \frac{c}{t_2}\right)$ is

The equation of the hyperbola,whose eccentricity is $\sqrt{2}$ and whose foci are $16$ units apart,is

At which point does the line $2x + \sqrt{6}y = 2$ touch the hyperbola $x^2 - 2y^2 = 4$?

If the line $x-1=0$ is a directrix of the hyperbola $kx^{2}-y^{2}=6$,then the hyperbola passes through which of the following points?

If $e_1$ and $e_2$ are respectively the eccentricities of the curves $9x^2 - 16y^2 - 144 = 0$ and $9x^2 - 16y^2 + 144 = 0$,then find the value of $\frac{e_1^2 e_2^2}{e_1^2 + e_2^2}$.