U6L6 Circles: Complete the Square

Here is an equation for a circle: x² + y² − 4x + 6y − 3 = 0. If we want to find the ​ (a)   of the circle, we can ​ (b)   in the form (x − h)² + (y − k)² = r². Start by ​ (c)   the terms in the equation to make it easier to work with. Group terms that include the​ (d)   and move the -3 to the​ (e)   of the equation.

x² − 4x + y² + 6y = 3

• rewrite the equation
• same variable
• right side
• center and radius
• rearranging

x² + y² − 4x + 6y − 3 = 0.

x² − 4x + y² + 6y = 3

We want the left side to include ​ (a)   —then, those trinomials can be rewritten in ​ (b)   to get the equation in the form we need. To create perfect square trinomials, we can ​ (c)   . We’ll keep the equation balanced by adding those same values to the ​ (d)   .

• 2 perfect square trinomials
• factored form
• add values to the left side
• other side

For the expression x² − 4x, we need to add ​ (a)   to get a perfect square trinomial. For the expression y² + 6y, we need to add ​ (b)   . Add these values to ​ (c)   of the equation. Then, ​ (d)   the numbers on the right side.

x² − 4x + 4 + y² + 6y + 9 = 3 + 4 + 9

x² − 4x + 4 + y² + 6y + 9 = ​ (e)  

• 4
• 9
• both sides
• combine
• 16

• squared binomials
• (2, − 3)

A circle has the equation (x - 2)² + (y + 3)² = 36. What are the coordinates of its center and the length of its radius?

• (-2, 3) and 6

• (2, -3) and 6

• (-2, 3) and 36

• (2, -3) and 36

Reorder the following: x² + y² - 2x + 6y + 3 = 0

• x²-2x+y²+6y=-3

• (x-1)²+(y+3)²=7

• x²-2x+1+y²+6y+9=-3+1+9

• x²-2x-1+y²+6y+9=7

What operation is performed to both sides of the equation to start solving it?

• Subtract 20

• Add 20

• Multiply by 20

• Divide by 20

What value is added to both sides of the equation to complete the square for y?

• 24

• 48

• 12

• 36

What is the radius of the circle after completing the square?

• 2

• 3

• 4

• 5

What are the coordinates of the center of the circle?

• (0, 0)

• (0, 6)

• (6, 0)

• (6, 6)