|
|
|
|
|
|
|
|
|
|
|
|
Identify the conic section $$$25 y^{2} = 1600 - 64 x^{2}$$$
Related calculators: Parabola Calculator, Circle Calculator, Ellipse Calculator, Hyperbola Calculator
Your Input
Identify and find the properties of the conic section $$$25 y^{2} = 1600 - 64 x^{2}$$$.
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, $$$A = 64$$$, $$$B = 0$$$, $$$C = 25$$$, $$$D = 0$$$, $$$E = 0$$$, $$$F = -1600$$$.
The discriminant of the conic section is $$$\Delta = 4 A C F - A E^{2} - B^{2} F + B D E - C D^{2} = -10240000$$$.
Next, $$$B^{2} - 4 A C = -6400$$$.
Since $$$B^{2} - 4 A C \lt 0$$$, the equation represents an ellipse.
To find its properties, use the ellipse calculator.
Answer
$$$25 y^{2} = 1600 - 64 x^{2}$$$A represents an ellipse.
General form: $$$64 x^{2} + 25 y^{2} - 1600 = 0$$$A.
Graph: see the graphing calculator.