Conic Sections - Maple Help

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Conic Sections

Main Concept

The conic sections are the curves formed by intersecting a cone with a plane. The four non-degenerate conics are the circle, the ellipse, the parabola, and the hyperbola:

 Circle Ellipse Parabola Hyperbola

The degenerate conics occur when the plane passes through the apex of the cone. These consist of the following types: a single point, a line, and the intersection of two lines.

Visualization: Intersection of a cone and with a plane

Use the sliders to manipulate the plane. See how the intersection with the cone changes to form a circle, ellipse, parabola, or a hyperbola.

 distance from origin =   angle  =



Visualization: General Form

The general form of a conic is:

 where A, B, C, D, E, F are real-valued parameters.

The classification of conics can be expressed using the following discriminants:

$\mathrm{Δ}=4ACF-A{E}^{2}+BE\mathrm{D}-{B}^{2}F-C{\mathrm{D}}^{2}$

 Conic Condition Circle , , and Ellipse , , and ( or ) Parabola , $\mathrm{Δ}\ne 0$ Hyperbola , $\mathrm{\Delta }\ne 0$ Line(s), Point $\mathrm{Δ}=0$

Use the sliders to modify coefficients of the general equation of a conic and see how it affects the conic        .

 A:  B: C: D: E: F: 

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