4xy+1.8y=27
You asked:
Investigate the equation: \(4 x y + 1.8 y = 27\).
MathBot Answer:
The graph of the equation \(4 x y + 1.8 y = 27\) is a hyperbola.
The coordinates of its foci are: \(\left(- \frac{3 \sqrt{6}}{2} - \frac{9}{20}, - \frac{3 \sqrt{6}}{2}\right)\) and \(\left(- \frac{9}{20} + \frac{3 \sqrt{6}}{2}, \frac{3 \sqrt{6}}{2}\right)\).
The coordinates of its vertices are: \(\left(- \frac{3 \sqrt{3}}{2} - \frac{9}{20}, - \frac{3 \sqrt{3}}{2}\right)\) and \(\left(- \frac{9}{20} + \frac{3 \sqrt{3}}{2}, \frac{3 \sqrt{3}}{2}\right)\).
The asymptotes have equations: \(- 60 \sqrt{3} x - 27 \sqrt{3} = 0\) and \(- 60 \sqrt{3} y = 0\).