4x*y+2x+2y=54
You asked:
Investigate the equation: \(4 x y + 2 x + 2 y = 54\).
MathBot Answer:
The graph of the equation \(4 x y + 2 x + 2 y = 54\) is a hyperbola.
The coordinates of its foci are: \(\left(- \frac{\sqrt{110}}{2} - \frac{1}{2}, - \frac{\sqrt{110}}{2} - \frac{1}{2}\right)\) and \(\left(- \frac{1}{2} + \frac{\sqrt{110}}{2}, - \frac{1}{2} + \frac{\sqrt{110}}{2}\right)\).
The coordinates of its vertices are: \(\left(- \frac{\sqrt{55}}{2} - \frac{1}{2}, - \frac{\sqrt{55}}{2} - \frac{1}{2}\right)\) and \(\left(- \frac{1}{2} + \frac{\sqrt{55}}{2}, - \frac{1}{2} + \frac{\sqrt{55}}{2}\right)\).
The asymptotes have equations: \(- \sqrt{55} x - \frac{\sqrt{55}}{2} = 0\) and \(- \sqrt{55} y - \frac{\sqrt{55}}{2} = 0\).