A circle has an equation of the following form.

It is a fact from geometry that given three noncollinear points—that is, points that do not all lie on the same straight line—there will be a circle that contains them. For example, the points (4, 2), (-5, -2), and (0, 3) lie on the circle whose equation is shown in the figure. Work Exercises in order, to find an equation of the circle passing through the points

Form a system of three equations using the answers from Exercises 51–53. Solve the system to find the values of a, b, and c.

Data from in Exercises 51–53

Let x = 2 and y = 1 in the general equation x² + y² + ax + by + c = 0 to find an equation in a, b, and c.

Let x = -1 and y = 0 to find a second equation in a, b, and c.

Let x = 3 and y = 3 to find a third equation in a, b, and c.

Transcribed Image Text:

x² + y² + ax + by + c = 0 Equation of a circle