xy -x – y = 1000
You asked:
Investigate the equation: \(x y - x - y = 1000\).
MathBot Answer:
The graph of the equation \(x y - x - y = 1000\) is a hyperbola.
The coordinates of its foci are: \(\left(1 - \sqrt{2002}, 1 - \sqrt{2002}\right)\) and \(\left(1 + \sqrt{2002}, 1 + \sqrt{2002}\right)\).
The coordinates of its vertices are: \(\left(1 - \sqrt{1001}, 1 - \sqrt{1001}\right)\) and \(\left(1 + \sqrt{1001}, 1 + \sqrt{1001}\right)\).
The asymptotes have equations: \(- 2 \sqrt{1001} x + 2 \sqrt{1001} = 0\) and \(- 2 \sqrt{1001} y + 2 \sqrt{1001} = 0\).