Lesson 5: 9-7 Equations of Circles

How can we check for reasonableness of this solution?

If the circle has center (-2,4) and passes through (-2,7), what is the equation for the circle?

If you can't remember the distance formula, is there another way to determine the radius of the circle?

After you find the center and radius, why is it good to find other points on the circle before you sketch it?

Is it possible to draw a perfect circle using just four points?

if you needed to know an exact point on a circle and it was not located at whole number coordinates, what is one way to find the coordinates?

How many times can a line intersect a circle?

compound locus

G.GPE.1 Derive the equation of a circle with given center and radius, using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.

An equation for a circle with center at (h,k) and radius of r units is (x-h)^2 + (y-k)^2 = r^2. The equation of a circle can be used to graph the circle on a coordinate plane. A circle can be graphed from three known points, and its equation can be found.

About 1000 tornadoes are reported across the United States each year. The most violent tornadoes have wind speeds of 250 mph or more. damage paths can be a mile wide and 50 miles long.

Tornado sirens are placed strategically on a circle around a town so they can be heard by all. Write the equation of the circle on which they are placed if the coordinated of the sirens are A(-8,3), B(-4,7), and C(-4,-1).

When using the distance formula, remind students to be careful to keep the x- and y-coordinates in the correct order and to keep track of their signs.

Logical Learners. Explain that students will rely heavily on their geometric knowledge and reasoning skills to solve the problems in this lesson. Allow students to explain how to explore and collaborate as they work through examples and exercises. Students need to recall definitions, concepts, and theorems to help explain why they use certain methods to solve problems.

Extension. What is the relationship between concentric circles with the same radius? Explain.

Formative assessment 

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