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WRITING EQUATIONS OF CIRCLES IN VERTEX FORM MM3G2
WRITING EQUATIONS OF CIRCLES IN VERTEX FORMMM3G2
Write the equation for the circle in vertex form:
Example 1
Step 1: Move the constant to the other side of the equation & put your common variables together
Example 1
Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. Both coefficients are 1 so divide
everything by 1
Example 1
Step 3: Group the x terms together and the y terms together using parenthesis.
Example 1
Step 4: Complete the square for the x terms
Then for the y terms
22=1 12=1 −42 =−2 (−2)2=4
Example 1
Step 5: Write the factored form for the groups.
What is the center of this circle?
What is the radius?
Write the equation for the circle in vertex form:
Example 2
Step 1: Move the constant to the other side of the equation & put your common variables together
Example 2
Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. Both coefficients are 2 so divide
everything by 2
Example 2
Step 3: Group the x terms together and the y terms together using parenthesis.
Example 2
Step 4: Complete the square for the x terms
Then for the y terms
62=3 32=9 42=2 22=4
Example 2
Step 5: Write the factored form for the groups.
What is the center of this circle?
What is the radius?
Write the equation for the circle in vertex form:
Example 3
Step 1: Move the constant to the other side of the equation & put your common variables together
Example 3
Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. Both coefficients are 4 so divide
everything by 4
Example 3
Step 3: Group the x terms together and the y terms together using parenthesis.
Example 3
Step 4: Complete the square for the x terms
Then for the y terms
62=3 32=9 82=4 42=16
Example 3
Step 5: Write the factored form for the groups.
What is the center of this circle?
What is the radius?
Write the equation for the circle in vertex form:
Example 4
Step 1: Move the constant to the other side of the equation & put your common variables together
Example 4
Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. Both coefficients are 5 so divide
everything by 5
Example 4
Step 3: Group the x terms together and the y terms together using parenthesis.
Example 4
Step 4: Complete the square for the x terms
Then for the y terms
−162 =−8¿ 4
2=2 22=4
Example 4
Step 5: Write the factored form for the groups.
What is the center of this circle?
What is the radius?
You Try! Write the following equation of a circle in
vertex form:
What is the center of this circle?What is the radius?
