Graphing Circles

Circle is a conic section with its both axes (major and minor) equal in length. The key features of a Circle are its radius (half of the measure of any axis or Diameter), its circumference, chords (diameter being the longest), center, arcs, sectors etc. In other words a circle can be defined as Set of all those points which are equidistant from center Point. Circles can also be defined by Intersection of a plane and a cone. Graphing circles means Graphing Equations of circles. General form of a circle equation is given as:
 
(x – h)² + (y – k)² = r² …..............equation 1.
 
Where,
h, k and c are constants (h and k being the coefficients).
'r' is Radius of Circle and point (h, k) represents the Center of Circle. For origin i.e. (0, 0) to be the center, values of 'h' and 'k' must be equals to zero giving simple equation for a circle.
(x – 0)² + (y – 0)² = r²,
(x)² + (y)² = r².
To graph equation 1, first plot the center i.e. (h, k). Next draw all points “r” units away from center by substituting values of 'x' for getting the corresponding values of 'y'. You can plot a few of them and then connect dots in a circular shape using a protractor.
Taking examples of two circles whose equations can be given as:
(x)² + (y)² = 25 and
(x - 4)² + (y - 4)² = 25
First equation has its origin at (0, 0) while second equation has its origin at (4, 4). Radii of both circles are equal. These circle equations can be graphed as follows as shown in figure: