1. College Algebra Chapter 2 Functions and Graphs
Section 2.2
Circles

2. 1. Write an Equation of a Circle in Standard Form
2. Write the General Form of an Equation of a Circle

3. Write an Equation of a Circle in Standard Form
A circle is the set of all points in a plane that are equidistant from a fixed point called the center.
The fixed distance from any point on the circle to the center is called the radius.

4. Write an Equation of a Circle in Standard Form
Standard Form of Equation of a Circle:
Center: ( h, k )
Radius: r (r > 0)

5. Write an Equation of a Circle in Standard Form
Example: Graph a circle with center ( –3, 2 ) and radius 4.
Equation:
Mark the center with an open circle.
Plot points 4 units up, down, left, and right
from the center.
Draw the circle through the points.

6. Example 1:
Write an equation of the circle in standard form and graph the circle.
Center: (0, –3) Radius: 2

7. Example 2:
Write an equation of the circle in standard form and graph the circle.
Center: (4, 3) Radius: 3

9. Example 3:
Write an equation of the circle in standard form and graph the circle.
The center is (3, –2) and the circle is tangent to the y-axis.

11. 1. Write an Equation of a Circle in Standard Form
2. Write the General Form of an Equation of a Circle

12. Write the General Form of an Equation of a Circle
General Form of Equation of a Circle:

13. Example 4:
Write the equation of the circle in general form:

14. Write the General Form of an Equation of a Circle
To write the equation of a circle from general form into standard form, we must complete the square twice.

15. Example:
Write the equation of the circle in standard form. Identify the center and radius.
Group the x terms, group the y terms.
Move the constant term to the right.

16. Example continued:
Complete the squares.
Identify center and radius from the equation.

17. Example 5:
Write the equation of the circle in standard form. Identify the center and radius.

18. Example 6:
Write the equation of the circle in standard form. Identify the center and radius.

20. Determining if an Equation Represents the Graph of a Circle
The equation represents a circle of radius r only if
If , then represents the single point (h, k). The solution set is { (h, k) }.
If , then the solution set is the empty set { }.

21. Example 7:
Determine if the equation represents the equation of a circle.

23. Graphing a Circle on a Calculator
A basic graphing calculator usually requires equations in the form y = ____________
Given:
Solve for y to obtain two equations

24. Graphing a Circle on a Calculator, continued
Enter each equation.
Graph on the standard viewing window.
The graph appears distorted because of the rectangular screen on the calculator.

25. Graphing a Circle on a Calculator, continued
To eliminate the distortion, go to the ZOOM menu and select ZSQUARE.

26. Graphing a Circle on a Calculator, continued
ZDECIMAL will also produce a "square" window, but it is considerably smaller.

27. Graphing a Circle on a Calculator, continued
We can zoom out once to see the entire graph.

28. Graphing a Circle on a Calculator, continued
We can also make our own custom window.