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

Use the values of a, b, and c from Exercise 54 and the form of the equation of a circle given above to write an equation of the circle passing through the given points.

Data from in Exercise 54

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.

Transcribed Image Text:

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