Math Problem Solver

The graph of the equation \(-\left( 8 z x \right) - 96 = -\left( 48 x \right)\) is a hyperbola.

The coordinates of its foci are: \(\left(- 2 \sqrt{6}, 2 \sqrt{6} + 6\right)\) and \(\left(2 \sqrt{6}, 6 - 2 \sqrt{6}\right)\).

The coordinates of its vertices are: \(\left(- 2 \sqrt{3}, 2 \sqrt{3} + 6\right)\) and \(\left(2 \sqrt{3}, 6 - 2 \sqrt{3}\right)\).

The asymptotes have equations: \(8 \sqrt{3} z - 48 \sqrt{3} = 0\) and \(- 8 \sqrt{3} x = 0\).