Equations of Circles 10.6 ESLRs: Becoming Effective Communicators, CA State Standards Lesson Goals 17: Prove theorems using coordinate geometry. Write the equation of a circle. Graph a circle on the coordinate plane. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

Previously on Geometry

definition Equation of a Circle On the coordinate plane a circle is defined by (x – h)2 + (y – k)2 = r2 (h, k) is the coordinate of the center r is the radius of the circle (x, y) r (h, k)

Give the center and radius of the circle

example Write the equation of a circle.

example Write the equation of a circle.

example Graph the circle: Center = Radius =

example Graph the circle: Center = Radius =

Example: solution graphically The equation of a circle is Are the following points on, inside or outside the circle? on C B A inside outside 8

solution algebraically (write in column) If you plug in a point (x, y) and then (x, y) is outside the circle then (x, y) is inside the circle then (x, y) is on the circle

Example: solution algebraically The equation of a circle is Are the following points on, inside or outside the circle? A on B C inside outside

Summary Explain the equation of a circle. How can you tell algebraically if a point is inside, on, or outside a circle?

Today’s Assignment p. 638: 8 – 40 e Tribe Pride always my best effort.

The rest at home Give the center and radius of the circle. Write the standard equation of the circle with the given center and radius. Use the given information to write the standard equation of the circle. Give the coordinates of the center, the radius, and the equation of the circle. Graph the equation. The rest at home