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This equation, known as the equation of the circle, ... plane can be broken into two semicircles each of which is the graph of a function, ...
Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a) 2 + (y − b) 2 = r 2 where a and b are the coordinates of the center (a, b) and r is the radius.
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
The equation defining a plane curve expressed in polar coordinates is known as a polar equation. In many cases, such an equation can simply be specified by defining r as a function of φ. The resulting curve then consists of points of the form (r(φ), φ) and can be regarded as the graph of the polar function r.
A circle with five chords and the corresponding circle graph. In graph theory, a circle graph is the intersection graph of a chord diagram.That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation + =. In general, every implicit curve is defined by an equation of the form (,) =
For example, the equations = = form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point.
(The generator circle is the inverse curve of the parabola's directrix.) This property gives rise to the following simple method to draw a cardioid: Choose a circle and a point on its perimeter, draw circles containing with centers on , and; draw the envelope of these circles.