a+ab+b=19

asked by guest
on Nov 25, 2024 at 3:52 am



You asked:

Investigate the equation: \(a + a b + b = 19\).

MathBot Answer:

The graph of the equation \(a + a b + b = 19\) is a hyperbola.

The coordinates of its foci are: \(\left(- 2 \sqrt{10} - 1, - 2 \sqrt{10} - 1\right)\) and \(\left(-1 + 2 \sqrt{10}, -1 + 2 \sqrt{10}\right)\).

The coordinates of its vertices are: \(\left(- 2 \sqrt{5} - 1, - 2 \sqrt{5} - 1\right)\) and \(\left(-1 + 2 \sqrt{5}, -1 + 2 \sqrt{5}\right)\).

The asymptotes have equations: \(- 4 \sqrt{5} a - 4 \sqrt{5} = 0\) and \(- 4 \sqrt{5} b - 4 \sqrt{5} = 0\).

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