All about circles

General equation of a circle:
The standard equation of a circle is an equation that when plotted on the co-ordinate plane results in a circular curve. The equation is as follows:
(x-h)^2 + (y-k)^2 = r^2
Where, (h,k) is the centre of the circle and r is the radius of the circle. For example if the centre of the circle is (2,-3) and radius is 4. Then the equation of the circle would be:
(x-2)^2 + (y+3)^2 = 16
The graph of the above circle would look like this:

Standard equation of circle:
A circle with centre a origin and radius r is called a standard circle. Therefore the equation of such a circle would be:
X^2 + y^2 = r^2
Where r = radius of the circle.
For example the standard equation of a circle with radius 3 would be:
X^2 +y^2 = 9
The graph of such a circle would look as follows:

Parametric equation of a circle:
If the parameter is an angle of measure t, then the parametric equation of a circle is given by:
X = r cos(t) and y = r Sin(t), where r = radius of the circle and the angle t ranges from 0 to 2 pi. For example the parametric equations of a circle with radius = 2 would be:
X = 2 cos(t) and y = 2 sin(t).
To be able to find the equation of a circle we need to know two things primarily, the centre of the circle and the radius. However for the standard equation only the radius need be known.

Circumference of Circle Equation:
Suppose there is a circular path around a lake. If we start moving from one point on the path in one direction, then since the path is circular we shall come back to our starting point. The distance thus covered by us in making this trip is called the circumference of the circle. There is no accurate measure of centre of a circle. If we wish to measure the circumference of the base of a cylinder, we can wind a thread around it, and then measure the length of the wound portion of the thread. However this practical method is not too useful for theoretical calculations. Moreover if we wish to find the circumference of very large cylindrical silos then this method is not even practical. The empirical formula derived by mathematicians for circumference of a circle is as follows:
C = 2pir, where r = radius of the circle.