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Identify the conic section $$$x^{2} = - 2 y^{2} + 4 y$$$
Related calculators: Parabola Calculator, Circle Calculator, Ellipse Calculator, Hyperbola Calculator
Your Input
Identify and find the properties of the conic section $$$x^{2} = - 2 y^{2} + 4 y$$$.
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, $$$A = 1$$$, $$$B = 0$$$, $$$C = 2$$$, $$$D = 0$$$, $$$E = -4$$$, $$$F = 0$$$.
The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = -16$$$.
Next, $$$B^{2} - 4 A C = -8$$$.
Since $$$B^{2} - 4 A C \lt 0$$$, the equation represents an ellipse.
To find its properties, use the ellipse calculator.
Answer
$$$x^{2} = - 2 y^{2} + 4 y$$$A represents an ellipse.
General form: $$$x^{2} + 2 y^{2} - 4 y = 0$$$A.
Graph: see the graphing calculator.