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Identify the conic section $$$\frac{615419 x^{2}}{10000} - \frac{7 x}{4} - \frac{9}{50000} = 0$$$
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Your Input
Identify and find the properties of the conic section $$$\frac{615419 x^{2}}{10000} - \frac{7 x}{4} - \frac{9}{50000} = 0$$$.
Solution
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, $$$A = \frac{615419}{10000}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = - \frac{7}{4}$$$, $$$E = 0$$$, $$$F = - \frac{9}{50000}$$$.
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.
Answer
$$$\frac{615419 x^{2}}{10000} - \frac{7 x}{4} - \frac{9}{50000} = 0$$$A represents a pair of the lines $$$x = - \frac{-43750 + \sqrt{1941756355}}{3077095}$$$, $$$x = \frac{43750 + \sqrt{1941756355}}{3077095}$$$A.
General form: $$$\frac{615419 x^{2}}{10000} - \frac{7 x}{4} - \frac{9}{50000} = 0$$$A.
Factored form: $$$\left(3077095 x - 43750 + \sqrt{1941756355}\right) \left(3077095 x - \sqrt{1941756355} - 43750\right) = 0.$$$A
Graph: see the graphing calculator.