4x*y+2x+2y+1=55

asked by guest
on Jan 23, 2025 at 6:41 pm



You asked:

Investigate the equation: \(4 x y + 2 x + 2 y + 1 = 55\).

MathBot Answer:

The graph of the equation \(4 x y + 2 x + 2 y + 1 = 55\) 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: \(- 2 \sqrt{55} x - \sqrt{55} = 0\) and \(- 2 \sqrt{55} y - \sqrt{55} = 0\).