1. Graph and Write Equations of Circles
Section 9.3
Graph and Write Equations of Circles

2. California Standard:
16.0: Students demonstrate and explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.

3. By following instructions, students will be able to:
OBJECTIVE(S):
By following instructions, students will be able to:
Graph and write equations of circles.

4. Standard Equation of a Circle with Center at the Origin: The standard form of the equation of a circle with center at (0,0) and radius r is as follows:

5. EXAMPLE 1:
Graph Identify the radius of the circle.

6. EXAMPLE 2:
The point (2,-5) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.

7. EXAMPLE 3:
What is an equation of the line tangent to the circle at (-3,2)?

8. U-TRY#1:
Graph the equation. Identify the radius of the circle. A) B) C)
Write the standard form of the equation of the circle that passes through (5,-1) and whose center is the origin.
Write an equation of the line tangent to the circle at (6,1)

9. Circle and Inequalities: If , then shade inside the circle
Circle and Inequalities: If , then shade inside the circle. If , then shade outside the circle.

10. EXAMPLE 4:
A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles east and 9 miles north of the tower. Are you in the tower’s range?

11. EXAMPLE 5:
In example 4, suppose that you fix your tire and then drive south. For how many more miles will you be in range of the tower?

12. HOMEWORK
Sec 9.3 WS