3ax-11=4(x+2)+2(x-1)
You asked:
Investigate the equation: \(3 a x - 11 = 4 \cdot \left(x + 2\right) + 2 \cdot \left(x - 1\right)\).
MathBot Answer:
The graph of the equation \(3 a x - 11 = 4 \cdot \left(x + 2\right) + 2 \cdot \left(x - 1\right)\) is a hyperbola.
The coordinates of its foci are: \(\left(2 - \frac{\sqrt{102}}{3}, - \frac{\sqrt{102}}{3}\right)\) and \(\left(2 + \frac{\sqrt{102}}{3}, \frac{\sqrt{102}}{3}\right)\).
The coordinates of its vertices are: \(\left(2 - \frac{\sqrt{51}}{3}, - \frac{\sqrt{51}}{3}\right)\) and \(\left(2 + \frac{\sqrt{51}}{3}, \frac{\sqrt{51}}{3}\right)\).
The asymptotes have equations: \(- 4 \sqrt{51} a + 8 \sqrt{51} = 0\) and \(- 4 \sqrt{51} x = 0\).