x+1.3x= X.4x-1
You asked:
Investigate the equation: \(x + 1.3 x = X \cdot .4 x - 1\).
MathBot Answer:
The graph of the equation \(x + 1.3 x = X \cdot .4 x - 1\) is a hyperbola.
The coordinates of its foci are: \(\left(\sqrt{5} + \frac{23}{4}, \sqrt{5}\right)\) and \(\left(\frac{23}{4} - \sqrt{5}, - \sqrt{5}\right)\).
The coordinates of its vertices are: \(\left(\frac{\sqrt{10}}{2} + \frac{23}{4}, \frac{\sqrt{10}}{2}\right)\) and \(\left(\frac{23}{4} - \frac{\sqrt{10}}{2}, - \frac{\sqrt{10}}{2}\right)\).
The asymptotes have equations: \(2 \sqrt{10} x = 0\) and \(4 \sqrt{10} X - 23 \sqrt{10} = 0\).