3xy + 1 = 2y - 5x

asked by guest
on Jan 22, 2025 at 4:14 pm



You asked:

Investigate the equation: \(3 x y + 1 = 2 y - 5 x\).

MathBot Answer:

The graph of the equation \(3 x y + 1 = 2 y - 5 x\) is a hyperbola.

The coordinates of its foci are: \(\left(\frac{2}{3} - \frac{\sqrt{26}}{3}, - \frac{5}{3} + \frac{\sqrt{26}}{3}\right)\) and \(\left(\frac{2}{3} + \frac{\sqrt{26}}{3}, - \frac{\sqrt{26}}{3} - \frac{5}{3}\right)\).

The coordinates of its vertices are: \(\left(\frac{2}{3} - \frac{\sqrt{13}}{3}, - \frac{5}{3} + \frac{\sqrt{13}}{3}\right)\) and \(\left(\frac{2}{3} + \frac{\sqrt{13}}{3}, - \frac{5}{3} - \frac{\sqrt{13}}{3}\right)\).

The asymptotes have equations: \(- 12 \sqrt{13} x + 8 \sqrt{13} = 0\) and \(12 \sqrt{13} y + 20 \sqrt{13} = 0\).

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