1. C I r c l e s

2. 8.3 Graph and Write Equations of Circles
Book Section 9.3

3. Circles center radius Take the square root!
The equation of a circle is:
center
Where (h, k) represent the ___________
and r is the _____________.
radius
How do you get the radius by itself?
Take the square root!

4. Ex 1: Graph the Equation of a Circle
Graph by finding the
center and radius of the circle.
Step 1: Identify the center & radius
(4, -2)
Center: ________ Radius: _________ 4
Step 2: Plot the center and then 4 points to the left, right, up, and down.

5. Ex 1: Graph the Equation of a Circle
Let’s take it one step further…What if I want
you to move the circle 3 units to the right and 4
units up? What would the equation be?
Step 1: Write the original equation
Step 2: Determine the new center after the shift.
(4, -2)
Center: _________
New Center: _____
(7, 2)
Step 3: Write the new equation

6. You Try… Graph the following: 1. 2. Center: ________ Center: ________
Center: ________ Center: ________
Radius: _________ Radius: ________
(0, 3)
(0, 0) 5 6

7. You Try… Graph the following: 3. 4. Center: ________ Center: ________
Center: ________ Center: ________
Radius: _________ Radius: ________
(-3, 2)
(3, 0)
≈ 3.162
≈ 2.828

8. Let’s Try the Reverse… Can you write an equation of a circle given the
center and radius?
Example: Write an equation for a circle with center C(-3, 6) and a radius of 6 units. Graph it.
Step 1: Write the standard form of the equation
Step 2: Label h, k, and r
h = k = r = 6
Step 3: Plug in your values and simplify!

9. You Try… Write the equation of the circle in standard
form. Then, graph it!
1. Center: (0, 0) and Center: (-3, 5) and radius of diameter of 8.

10. Practice What is an equation of the line tangent to the
circle at (-1, 3)?
What is a tangent????
Remember, we learned in Geometry that a tangent to a circle is ______________ to the radius at a point of tangency.
perpendicular
Step 1: Graph the circle

11. Practice What is an equation of the line tangent to the
circle at (-1, 3)?
Step 2: Plot the point (-1,3) and determine the slope of the radius. How will you do this?
Step 3: What will the slope be of a line perpendicular to the radius?

12. TAKS Practice What is an equation of the line tangent to the
circle at (-1, 3)?
Step 4: Use point-slope form to find the equation using point (-1,3) and slope of 1/3.

13. Completing the Square Put in ax2 + bx + c = 0 form
Add/Subtract the c to the other side of the equation
If needed find the GCF (a has to be 1)
Half the b value and square it, and give that value to both sides of the equation.
Write the trinomial as a binomial squared.

14. Try using completing the Square
x2 – 6x – 4 = 0
x2 + 8x + 12 = 0
3x2 + 12x – 5 = 0

15. Standard Form  Center Form
Change into center form. Use completing the square!
Step 1: Write the equation with the number without the variable on the other side of the equal sign.
Step 2: Group your variables together if they are not already. (in this case, they are!)

16. Standard Form  Center Form
Step 3: Complete the square for each one! 9 16 9 16
Step 4: Write each as a polynomial squared:
Step 5: Identify the center and radius and graph it!
Center =
Radius =

17. Try these…
What is an equation of the line tangent to the circle at (-4, 7)?
Change into center form.

19. In Class Assignment Homework Worksheet Page 629
# 3, 5, 9, 11, 15, 17, 23, 25, 31 33