Circle illustration showing a
radius, a diameter, the centre and the circumference
A circle is a simple shape of Euclidean
geometry consisting of the set of points in a plane that is a given distance from a given
point, the centre. The distance between any of the points and the centre is
called the radius.
Circles are simple closed curves which divide the plane into two regions: an interior and an exterior. In everyday use, the
term "circle" may be used interchangeably to refer to either the
boundary of the figure, or to the whole figure including its interior; in
strict technical usage, the circle is the former and the latter is called a disk.
A circle is a special ellipse in which the two foci are
coincident and the eccentricity is 0. Circles are conic sections attained when a right circular cone is intersected by a plane
perpendicular to the axis of the cone.
Equation
Cartesian coordinates
Circle
of radius r = 1,
centre (a, b) = (1.2,
−0.5)
In an x-y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that
This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as
shown in the diagram to the right, the radius is the hypotenuse of a
right-angled triangle whose other sides are of length x − a and y − b. If the circle is centered
at the origin (0, 0), then the equation simplifies to
In homogeneous coordinates each conic section with equation of a circle is
of the form
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Circle
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