Identify the conic section $$$\frac{3 x y}{2} = 40$$$

Identify and find the properties of the conic section $$$\frac{3 x y}{2} = 40$$$.

The general equation of a conic section is $$$A x^{2} + B x y + C y^{2} + D x + E y + F = 0$$$.

In our case, $$$A = 0$$$, $$$B = \frac{3}{2}$$$, $$$C = 0$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = -40$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 90$$$.

Next, $$$B^{2} - 4 A C = \frac{9}{4}$$$.

Since $$$B^{2} - 4 A C \gt 0$$$, the equation represents a hyperbola.

To find its properties, use the hyperbola calculator.

$$$\frac{3 x y}{2} = 40$$$A represents a hyperbola.

General form: $$$\frac{3 x y}{2} - 40 = 0$$$A.

Graph: see the graphing calculator.