xy - 9 = 5*xy - 3
You asked:
Investigate the equation: \(x y - 9 = 5 \cdot x y - 3\).
MathBot Answer:
The graph of the equation \(x y - 9 = 5 \cdot x y - 3\) is a hyperbola.
The coordinates of its foci are: \(\left(- \sqrt{3}, \sqrt{3}\right)\) and \(\left(\sqrt{3}, - \sqrt{3}\right)\).
The coordinates of its vertices are: \(\left(- \frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right)\) and \(\left(\frac{\sqrt{6}}{2}, - \frac{\sqrt{6}}{2}\right)\).
The asymptotes have equations: \(2 \sqrt{6} y = 0\) and \(- 2 \sqrt{6} x = 0\).