x+3xy+y=12
You asked:
Investigate the equation: \(x + 3 x y + y = 12\).
MathBot Answer:
The graph of the equation \(x + 3 x y + y = 12\) is a hyperbola.
The coordinates of its foci are: \(\left(- \frac{\sqrt{74}}{3} - \frac{1}{3}, - \frac{\sqrt{74}}{3} - \frac{1}{3}\right)\) and \(\left(- \frac{1}{3} + \frac{\sqrt{74}}{3}, - \frac{1}{3} + \frac{\sqrt{74}}{3}\right)\).
The coordinates of its vertices are: \(\left(- \frac{\sqrt{37}}{3} - \frac{1}{3}, - \frac{\sqrt{37}}{3} - \frac{1}{3}\right)\) and \(\left(- \frac{1}{3} + \frac{\sqrt{37}}{3}, - \frac{1}{3} + \frac{\sqrt{37}}{3}\right)\).
The asymptotes have equations: \(- 12 \sqrt{37} x - 4 \sqrt{37} = 0\) and \(- 12 \sqrt{37} y - 4 \sqrt{37} = 0\).