Conic sections

The conic sections may be defined in several ways :
Section of a circular cone by a plane (hence the name).
Algebraic curve with degree 2 (equation ax² + bxy + cy² + dx + ey + f = 0).
Locus of points and envelopes.

Focus properties of conic sections

Focus definition.
Circles and directrix lines.
Parameter. Excentricity.
Conic sections as locus of points.
Tangents to conic sections. Conic sections as envelopes of lines.
    Constructions
    Construct a conic section, given etc...

Parabola

Specific case of parabola.
    Constructions

Stretch properties of ellipse

Ellipse considered as a stretched circle.

Hyperbola

Properties of asymptotes.

Conic sections in projective geometry

Conic section defined by 5 points.
Homography and Co
Pascal theorem ...
    Pencils of conic sections and applications.
    Constructions (intersections).
    Constructions (conic section defined by ...).

 

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