Elementary Curves
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.
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)
