Equations of circles

Teacher tools for this standard

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.

G 609. Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle) G 605. Use the distance formula AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c G 701. Use relationships among angles, arcs, and distances in a circle

G 609. Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)
G 605. Use the distance formula
AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c
G 701. Use relationships among angles, arcs, and distances in a circle

What you'll learn

Write the standard form (x - h)^2 + (y - k)^2 = r^2 and explain it as the distance formula with the distance held fixed at r
Read the center and the radius off an equation already in standard form, handling both the sign inversion on h and k and the square on r
Write the equation of a circle from a stated center and radius, and from indirect information -- a point on the circle, or the endpoints of a diameter
Convert an expanded general-form circle equation to standard form by completing the square in x and in y
Identify an equation as a circle by checking that both squared terms are present with equal, same-signed coefficients

Review first:

Slides

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