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.
Nondegenerate Conics
Ellipse
x^{2 }/ a^{2} + y^{2 }/ b^{2} = 1 (1)
where
a, b = intrinsic parameters
Circle
Circle, a special ellipse, can be expressed as
x^{2} + y^{2 }= a^{2} (2)
where
a = radius
Hyperbola
x^{2 }/ a^{2}  y^{2 }/ b^{2} = 1 (3)
where
a, b = intrinsic parameters
Parabola
y^{2}  2 l x = 0 (4)
where
l = intrinsic parameter
Degenerate Conics
Parallel Lines
x^{2}  a^{2} = 0 (5)
where
a = half the distance between the parallel lines
Intersecting Lines
x^{2 }/ a^{2}  y^{2 }/ b^{2} = 0 (6)
where
tan^{1}(b/a) = half the angle between the intersecting lines
Coincident Lines
x^{2} = 0 (7)
Related Topics

Mathematics
Mathematical rules and laws  numbers, areas, volumes, exponents, trigonometric functions and more.
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