Lesson Plan: Intersections of Circles and Lines Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find points of intersection of circles and lines.
Students will be able to
- understand that a line can intersect a circle at two points, touch it at one point, or not intersect it at all,
- find how many times a line intersects a circle, given in standard or general form, by using properties of the discriminant or otherwise,
- find the coordinates of the points at which a line intersects a circle, if they exist,
- solve algebraic problems involving the intersection of circles and lines.
Students should already be familiar with
- equations of circles,
- finding the intersection points of graphs of functions.
Students will not cover
- properties of tangents and chords.