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Elementary Curves
Ellipse, Circle, Hyperbola, Parabola - Parallel, Intersecting and Coincident Lines
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The simplest curve is the straight line. The next 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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