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Example:Finding Equation of Circle

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Explanation:

 

Circle

 

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

 

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.