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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

#### 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

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

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## Citation

• Engineering ToolBox, (2009). Elementary Curves. [online] Available at: https://www.engineeringtoolbox.com/elementary-curves-d_1472.html [Accessed Day Mo. Year].

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