NUMBAT OER - Open Educational Resources

2.2 Circles and ellipses

Acircle is the shape defined by the path of a point moving at a constant distance from another point. The constant distance is termed the 'radius' of the circle. An ellipse is oval in shape, which also comprises a single line which has no ends (ie it joins onto itself) and is defined by a major and minoraxis. Acircleisaspecialcaseofanellipse,wherethelengthsofthetwoaxesareidentical.

The quantity π used in the following formulae is the ratio between the perimeter of a circle and its diameter (the distance from one side of a circle to the other passing through the centre, or twice the value of the radius).

Shape perimeter Area
Circle
(the distances from the centre to the edge of the circle is the same in all directions)
2 πr πr2
Ellipse
(a 'squashed' circle or oval, defined by the lengths of its major and minor axes)

2π (0.5 . x2 . y2)0.5

(see note below)

πxy

Note: the formula for the perimeter of an ellipse is an approximation