Elementary Curves

Ellipse, circle, hyperbola, parabola, parallel and 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


x2 / a2 + y2 / b2 = 1                                     (1)


a, b = intrinsic parameters


Circle, a special ellipse, can be expressed as

x2 + y2 = a2                                          (2)


a = radius


x2 / a2 - y2 / b2 = 1                                    (3)


a, b = intrinsic parameters


y2 - 2 l x = 0                                     (4)


l = intrinsic parameter

Degenerate Conics

Parallel Lines

x2 - a2 = 0                                  (5)


a = half the distance between the parallel lines

Intersecting Lines

x2 / a2 - y2 / b2 = 0                               (6)


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

Tag Search

  • en: elementary curves ellipse circle hyperbola parabola parallel lines intersecting coincident
  • es: curvas elementales círculo elipse hipérbola parábola líneas paralelas se cruzan coincidente
  • de: Elementarkurven Ellipse Hyperbel Parabel Kreis parallelen Linien zusammenfällt schneid

Search the Engineering ToolBox

- "the most efficient way to navigate!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!