The equation of the director circle of the hyperbola $\frac{x^2}{16} - \frac{y^2}{4} = 1$ is given by

Find the equation of the hyperbola satisfying the given conditions: Foci $(\pm 4, 0)$,the latus rectum is of length $12$.

If the latus rectum of a hyperbola through one focus subtends an angle of $60^{\circ}$ at the other focus,then its eccentricity is

The equation of the pair of asymptotes of the hyperbola $\frac{(x-3)^2}{3}-\frac{(y-2)^2}{2}=1$ is

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?

If the line $5x - 2y - 6 = 0$ is a tangent to the hyperbola $5x^2 - ky^2 = 12$,then the equation of the normal to this hyperbola at the point $(\sqrt{6}, p)$ where $p < 0$ is: