The values of $m$ for which the line $y=mx+2$ is a tangent to the hyperbola $4x^2-9y^2=36$ are

If the equation of a hyperbola is $9x^2 - 16y^2 + 72x - 32y - 16 = 0$,then the equation of its conjugate hyperbola is

If the line $lx + my = 1$ is a normal to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,then $\frac{a^2}{l^2} - \frac{b^2}{m^2}$ is equal to

If a circle cuts a rectangular hyperbola $xy = c^2$ at four points $A, B, C,$ and $D$,and the parameters of these four points are $t_1, t_2, t_3,$ and $t_4$ respectively,then which of the following is true?

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 the other asymptote is:

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?