Derive circle equation

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Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

HSG.GPE.A.1

**HSG.GPE.A.1**: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

HSG.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

What you'll learn

Derive the equation of a circle with center (h, k) and radius r using the Pythagorean Theorem and the distance formula
Write the equation of a circle in standard form: (x - h)^2 + (y - k)^2 = r^2
Identify the center and radius of a circle given its equation in standard form
Complete the square to convert a circle's equation from general form (expanded) to standard form
Find the center and radius of a circle given by an equation in general form
Explain why the equation (x - h)^2 + (y - k)^2 = r^2 represents all points at distance r from (h, k)

Review first:

Slides

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Derive circle equation

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Completing the square

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Practice

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Exercise

Practice problems, checked as you go

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