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. 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.

 

The general form of a conic is:

Ax2 +Bxy +Cy2 +Dx +Ey+F = 0

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

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

 

B24 A C

Δ=4ACFAE2+BEDB2FCD2

 

Conic

Condition

Circle

B =0, A =C, and C Δ > 0

Ellipse

B24 AC  <0, C Δ &gt; 0, and (B 0 or A C)

Parabola

B24 AC  &equals;  0 , &Delta;0

Hyperbola

B2 4 AC &gt; 0, Δ0

Line(s), Point

&Delta;&equals;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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