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