Lesson Plan: Equation of a Circle Mathematics • 11th Grade

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the equation of a circle using its center and a given point or the radius and vice versa.

Objectives

Students will be able to

  • derive and recall the standard form of the equation of a circle, (𝑥−𝑎)+(𝑦−𝑏)=𝑟, and the general form, 𝑎𝑥+𝑏𝑦+𝑐𝑥+𝑑𝑦+𝑒=0,
  • write the equation of a circle in standard form and general form given its center and its radius, or a point on its circumference,
  • find the center of a circle and its radius given its equation in standard form,
  • find the center of a circle and its radius given its equation in expanded form (by completing the square),
  • find the equation of a circle given a wider geometric context such as the equation of a line that contains its center and points on its circumference.

Prerequisites

Students should already be familiar with

  • the Pythagorean theorem,
  • how to complete the square.

Exclusions

Students will not cover

  • the vector form or parametric form of a circle.

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