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

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

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

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = \frac{4}{3}$$$.

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

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

To find its properties, use the hyperbola calculator.

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

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

Graph: see the graphing calculator.