Identify the conic section $$$\frac{9 x}{10} = \frac{224}{5} - \frac{23 x^{2}}{10}$$$

Identify and find the properties of the conic section $$$\frac{9 x}{10} = \frac{224}{5} - \frac{23 x^{2}}{10}$$$.

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, $$$A = \frac{23}{10}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = \frac{9}{10}$$$, $$$E = 0$$$, $$$F = - \frac{224}{5}$$$.

The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = 0$$$.

Next, $$$B^{2} - 4 A C = 0$$$.

Since $$$\Delta = 0$$$, this is the degenerated conic section.

Since $$$B^{2} - 4 A C = 0$$$, the equation represents two parallel lines.

$$$\frac{9 x}{10} = \frac{224}{5} - \frac{23 x^{2}}{10}$$$A represents a pair of the lines $$$x = - \frac{9 + \sqrt{41297}}{46}$$$, $$$x = \frac{-9 + \sqrt{41297}}{46}$$$A.

General form: $$$\frac{23 x^{2}}{10} + \frac{9 x}{10} - \frac{224}{5} = 0$$$A.

Factored form: $$$\left(46 x + 9 + \sqrt{41297}\right) \left(46 x - \sqrt{41297} + 9\right) = 0$$$A.

Graph: see the graphing calculator.