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Identify the conic section $$$- 2 x y + 5 y^{2} - 2 = 0$$$
Related calculators: Parabola Calculator, Circle Calculator, Ellipse Calculator, Hyperbola Calculator
Your Input
Identify and find the properties of the conic section $$$- 2 x y + 5 y^{2} - 2 = 0$$$.
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, $$$A = 0$$$, $$$B = 2$$$, $$$C = -5$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = 2$$$.
The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = -8$$$.
Next, $$$B^{2} - 4 A C = 4$$$.
Since $$$B^{2} - 4 A C \gt 0$$$, the equation represents a hyperbola.
To find its properties, use the hyperbola calculator.
Answer
$$$- 2 x y + 5 y^{2} - 2 = 0$$$A represents a hyperbola.
General form: $$$2 x y - 5 y^{2} + 2 = 0$$$A.
Graph: see the graphing calculator.