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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)

Related Topics

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

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