1. 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

2. Previously on Geometry

3. 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)

4. Give the center and radius of the circle

5. example
Write the equation of a circle.

6. example
Write the equation of a circle.

7. example
Graph the circle:
Center = Radius =

8. example
Graph the circle:
Center = Radius =

9. 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

10. 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

11. 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

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

13. Today’s Assignment
p. 638: 8 – 40 e
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14. 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