Writing equations of circles in vertex form

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?