(2x+1)(y-3)=1
You asked:
Investigate the equation: \(\left(2 x + 1\right) \cdot \left(y - 3\right) = 1\).
MathBot Answer:
The graph of the equation \(\left(2 x + 1\right) \cdot \left(y - 3\right) = 1\) is a hyperbola.
The coordinates of its foci are: \(\left(- \frac{3}{2}, 2\right)\) and \(\left(\frac{1}{2}, 4\right)\).
The coordinates of its vertices are: \(\left(- \frac{\sqrt{2}}{2} - \frac{1}{2}, 3 - \frac{\sqrt{2}}{2}\right)\) and \(\left(- \frac{1}{2} + \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} + 3\right)\).
The asymptotes have equations: \(- 2 \sqrt{2} x - \sqrt{2} = 0\) and \(- 2 \sqrt{2} y + 6 \sqrt{2} = 0\).