Circle Equations and Completing the Square

This video tutorial demonstrates how to find the center and radius of a circle by completing the square. The process begins with simplifying the given equation by dividing all terms by four. Next, the terms are regrouped to separate x and y components. The instructor then completes the square for both x and y terms, adding necessary constants to both sides of the equation. Finally, the equation is rewritten in center-radius form, revealing the circle's center and radius.

What is the first step taken to simplify the equation 4x^2 + 4y^2 - 16x + 24y - 36?

• Subtract 36 from both sides

• Divide all terms by 4

• Divide all terms by 2

• Multiply all terms by 4

After dividing all terms by 4, what is the resulting equation?

• x^2 + y^2 - 8x + 12y - 18 = 0

• x^2 + y^2 - 4x + 6y - 9 = 0

• 4x^2 + 4y^2 - 16x + 24y - 36 = 0

• x^2 + y^2 - 2x + 3y - 4.5 = 0

What is the next step after simplifying the equation by dividing all terms by 4?

• Add 9 to both sides

• Group x and y terms together

• Combine like terms

• Factor out common terms

What is the coefficient of the linear x term after grouping the x terms together?

• -2

• 2

• -4

• 4

What value is added inside the parentheses when completing the square for the x terms?

• 4

• 2

• -2

• -4

What is the value of (1/2 of -4)^2?

• 4

• -2

• 16

• 2

What value is added inside the parentheses when completing the square for the y terms?

• 9

• 12

• 3

• 6

What is the value of (1/2 of 6)^2?

• 12

• 9

• 6

• 3

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

• (3, -2)

• (2, -3)

• (-3, 2)

• (-2, 3)

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

• √44

• 2√11

• √22

• √11