Identify the conic section $$$\frac{197 x^{2}}{625} = \frac{1}{25000000}$$$
Related calculators: Parabola Calculator, Circle Calculator, Ellipse Calculator, Hyperbola Calculator
Your Input
Identify and find the properties of the conic section $$$\frac{197 x^{2}}{625} = \frac{1}{25000000}$$$.
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, $$$A = \frac{197}{625}$$$, $$$B = 0$$$, $$$C = 0$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = - \frac{1}{25000000}$$$.
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
$$$\frac{197 x^{2}}{625} = \frac{1}{25000000}$$$A represents a pair of the lines $$$x = - \frac{\sqrt{197}}{39400}$$$, $$$x = \frac{\sqrt{197}}{39400}$$$A.
General form: $$$\frac{197 x^{2}}{625} - \frac{1}{25000000} = 0$$$A.
Factored form: $$$\left(39400 x - \sqrt{197}\right) \left(39400 x + \sqrt{197}\right) = 0$$$A.
Graph: see the graphing calculator.