(e) Find all solution of the given equation x* - 2a + 1 = 0
You asked:
Investigate the equation: \(x \cdot -\left( 2 a \right) + 1 = 0\).
MathBot Answer:
The graph of the equation \(x \cdot -\left( 2 a \right) + 1 = 0\) is a hyperbola.
The coordinates of its foci are: \(\left(1, 1\right)\) and \(\left(-1, -1\right)\).
The coordinates of its vertices are: \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\) and \(\left(- \frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2}\right)\).
The asymptotes have equations: \(2 \sqrt{2} x = 0\) and \(2 \sqrt{2} a = 0\).