Lesson: Equation of a Circle Passing through Three Noncollinear Points Mathematics • 11th Grade

In this lesson, we will learn how to find the equation of a circle passing through three noncollinear points that form a right triangle.

Lesson Plan

Students will be able to

understand the geometric construction for drawing a circle through three points using perpendicular bisectors,
use three points on the circumference of a circle that form a right triangle to find
- the coordinates of the center of the circle,
- the radius of the circle,
- the equation of the circle.

Q1:

Find the equation of the circle that passes through the points , , and .

Q2:

Determine the general equation of the shown circle passing through the origin point and the two points and .

Q3:

Find the general equation of the circle through the origin that also passes through and .