13x-11y=6xy
You asked:
Investigate the equation: \(13 x - 11 y = 6 x y\).
MathBot Answer:
The graph of the equation \(13 x - 11 y = 6 x y\) is a hyperbola.
The coordinates of its foci are: \(\left(- \frac{\sqrt{286}}{6} - \frac{11}{6}, \frac{13}{6} + \frac{\sqrt{286}}{6}\right)\) and \(\left(- \frac{11}{6} + \frac{\sqrt{286}}{6}, \frac{13}{6} - \frac{\sqrt{286}}{6}\right)\).
The coordinates of its vertices are: \(\left(- \frac{\sqrt{143}}{6} - \frac{11}{6}, \frac{\sqrt{143}}{6} + \frac{13}{6}\right)\) and \(\left(- \frac{11}{6} + \frac{\sqrt{143}}{6}, \frac{13}{6} - \frac{\sqrt{143}}{6}\right)\).
The asymptotes have equations: \(6 \sqrt{143} y - 13 \sqrt{143} = 0\) and \(- 6 \sqrt{143} x - 11 \sqrt{143} = 0\).