Solve fraction numerator x minus 5 over denominator 2 end fraction equals blank fraction numerator x plus 2 over denominator 6 end fraction minus 3.
You asked:
Investigate the equation: \(\frac{x - 5}{2} = blank \cdot \frac{x + 2}{6} - 3\).
MathBot Answer:
The graph of the equation \(\frac{x - 5}{2} = blank \cdot \frac{x + 2}{6} - 3\) is a hyperbola.
The coordinates of its foci are: \(\left(3 - \sqrt{6}, -2 + \sqrt{6}\right)\) and \(\left(\sqrt{6} + 3, - \sqrt{6} - 2\right)\).
The coordinates of its vertices are: \(\left(3 - \sqrt{3}, -2 + \sqrt{3}\right)\) and \(\left(\sqrt{3} + 3, -2 - \sqrt{3}\right)\).
The asymptotes have equations: \(2 \sqrt{3} x + 4 \sqrt{3} = 0\) and \(- 2 \sqrt{3} blank + 6 \sqrt{3} = 0\).