Creating Circle Equations
When Center and Radius Are Known
One way to generate a circle's equation, is to fill in the standard form with the center values and its radius.
(x h)² + (y k)² = radius²
'h' and 'k' are usually used to denote a circle's center.
For Example:
What is the equation of a circle whose center is (3, 4) and the radius is 2?
Filling in this equation:
(x h)² + (y k)² = radius²
we get:
(x 3)² + (y  4)² = 2²
which equals
(x 3)² + (y +4)² = 4
which is the standard form of the equation
If we multiply this, it becomes the general form of the circle's equation.
x² 6x + 9 + y² + 8y +16 =4
which equals
x² + y² 8x + 6y +21 = 0
When Three Points Are Known
When you are given three points not in a straight line
for example, (9, 2) (3, 4) and (5, 6)
click here to see the procedure for generating the circle's equation.

