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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.

## Related Documents

• ### Area of Intersecting Circles

Calculate area of intersecting circles
• ### Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.
• ### Circle - Equation

The equation for a circle
• ### Circle - the Chord Lengths when Divided in to Equal Segments

Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.
• ### Circles - Circumferences and Areas

Circumferences and areas of circles with diameters in inches.
• ### Circles Outside a Circle

Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.
• ### Circles within a Rectangle - Calculator

Calculate the maximum number of circles within a rectangle - can be used to calculate the numbers of pipes or wires in a conduit or similar.
• ### Elementary Surfaces

Ellipsoid, sphere, hyperboloid, cone and more.
• ### Equal Areas - Circles vs. Squares

Radius and side lengths of equal areas, circles and squares.
• ### Geometric Shapes - Areas

Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..
• ### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.
• ### Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.

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## Citation

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

Modify the access date according your visit.

10.2.10