1. 5.2 Graph and Write Equations of Circles
Pg 180

2. A circle is an infinite set of points in a plane that are equal distance away from a given fixed point called a center.
A radius is a segment that connects the center and one of the points on the circle.
Every radius is equal in length. (radii)
A diameter is a line segment that connects two points on the circle and goes through the center.

3. The formula for a circle with its center at (0,0) and a radius of “r” is:
Example: What is the equation for a circle whose center is at (0,0) and has a radius of 6.
Answer ?

4. Example #2: Identify the center and the radius of the following:
Answer ?
Center:
(0,0)
Radius 10

5. Write an equation for the following in standard form.

6. Graph the Equation of a Circle
Graph x2 = 25 – y2

7. Write an Equation of a Circle
The point (6, 2) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.
We need to find the radius.
Use the distance formula.

8. If a circle has a translated center then the new equation will be:
Where the new center will be (h, k) and “r” will be the radius.

9. Example #1. Write the standard equation for a circle whose center is at (-3,5) and has a radius of 7.
Answer: Since h=-3 and k=5 and r=7 we can substitute these into the equation
Therefore:
Or:

10. Example #2 Given the following equation, identify the center and the radius.
Did you say (7,-2)
Radius ?
I bet you said (drum roll please) 9
You guys are AWESOME !!!

11. Example #3 Given the following graph answer the following questions.
1. Identify the center.
2. Name the radius.
3. Write an equation in standard form for the circle.

13. Answers
Center: (-2,-1)
Radius: 8
Equation:

14. Finding the equation of a Tangent Line to a Circle
Any line tangent to a circle will be perpendicular to a line that goes through the tangent point and the center of the circle
Perpendicular lines have negative reciprocal slopes
(Opposite Reciprocal)
So if we have the center of a circle, and the point of tangency, we can find the slope by the slope formula
Take the negative reciprocal and use the point slope formula for a line that goes through the tangent point

15. Find the equation of a Tangent Line to a circle
Find the equation of a tangent line to the circle x2 + y2 = 10 at (-1, 3)

16. Assignment
Pg 182
1 – 23, 24 odd
Pg 183
1 – 17, 18 odd