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Elementary Curves

Ellipse, circle, hyperbola, parabola, parallel and intersecting and coincident lines

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The simplest of all curves are the straight lines. The next in complexity are the second degree or conics curves.

Non-degenerate Conics

Ellipse

x2 / a2 + y2 / b2 = 1                                     (1)

where

a, b = intrinsic parameters

Circle

Circle, a special ellipse, can be expressed as

x2 + y2 = a2                                          (2)

where

a = radius

Hyperbola

x2 / a2 - y2 / b2 = 1                                    (3)

where

a, b = intrinsic parameters

Parabola

y2 - 2 l x = 0                                     (4)

where

l = intrinsic parameter

Degenerate Conics

Parallel Lines

x2 - a2 = 0                                  (5)

where

a = half the distance between the parallel lines

Intersecting Lines

x2 / a2 - y2 / b2 = 0                               (6)

where

tan-1(b/a) = half the angle between the intersecting lines

Coincident Lines

x2 = 0                                       (7)

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  • de: Elementarkurven Ellipse Hyperbel Parabel Kreis parallelen Linien zusammenfällt schneid
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