9.10Circles in the Coordinate Plane
Quick Answer
To determine whether a point (x, y) is inside, on, or outside a circle (x−h)² + (y−k)² = r²: substitute the point and compare the result to r². Less than r² → inside; equal → on; greater → outside.
Essential Question
How does the equation of a circle allow you to determine the position of any point relative to the circle without graphing?
Learning Goals
- 1Graph a circle given its equation in standard form.
- 2Determine whether a point is inside, on, or outside a circle.
- 3Find the equation of a circle given a center and a point on the circle.
- 4Solve applied problems involving circles in the coordinate plane.
Key Vocabulary
Interior of a circle
The set of all points whose distance from the center is less than the radius.
Exterior of a circle
The set of all points whose distance from the center is greater than the radius.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.