Lesson Plan

Move between a circle's equation and its center, radius, and graph in either direction: write (x - h)^2 + (y - k)^2 = r^2 from a center and radius or from the endpoints of a diameter, and read the center (h, k) and radius r from a standard-form equation

Convert a circle equation from general form (x^2 + y^2 + Dx + Ey + F = 0) to standard form by completing the square

Graph a circle on the coordinate plane by plotting the center and using the radius

Decide whether a point lies on, inside, or outside a circle by comparing its squared distance from the center with r^2

Describe how a change to a circle's equation changes its graph, and how a change to the graph changes the equation

"Create an equation to represent a circle in the xy-plane." "Describe how a change to the equation representing a circle affects the graph of the circle in the xy-plane or how a change to the graph of a circle affects the equation that represents the circle." "Understand that the ordered pairs that satisfy an equation of the form (x - h)^2 + (y - k)^2 = r^2 form a circle when plotted in the xy-plane." "Complete the square in an equation representing a circle to determine properties of the circle when it is graphed in the xy-plane and use the distance formula in problems related to circles."