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 equationIf 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 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.