Completing the Square Method for Finding the Center and Radius of a Circle

The video tutorial explains the different forms of circle equations, including the basic form centered at the origin and the expanded form. It demonstrates how to find the center and radius of a circle using two methods: comparison with the general equation and completing the square. The tutorial provides examples to illustrate both methods, emphasizing the importance of understanding the relationship between the equation's coefficients and the circle's properties.

Which of the following is the equation of a circle centered at the origin?

• X^2 + Y^2 = R^2

• X^2 + Y^2 + 2GX + 2FY + C = 0

• X - A^2 + Y - B^2 = R^2

• X^2 + Y^2 + AX + BY + C = 0

In the expanded equation X^2 + Y^2 - 8X + 2Y + 13 = 0, what is the value of G?

• 4

• -4

• 8

• -8

What is the center of the circle for the equation X^2 + Y^2 - 8X + 2Y + 13 = 0 using the comparative method?

• (1, -4)

• (-4, 1)

• (-1, 4)

• (4, -1)

What is the first step in completing the square for the equation X^2 + Y^2 - 8X + 2Y + 13 = 0?

• Rearrange and group terms

• Multiply by a constant

• Solve for Y

• Add 13 to both sides

After completing the square, what is the radius of the circle for the equation X^2 + Y^2 - 8X + 2Y + 13 = 0?

• 2

• 4

• 3

• 1

In the equation 2X^2 + 2Y^2 - 8X + 5Y + 10 = 0, what is the value of F using the comparative method?

• 1/2

• 2

• 5/2

• 5/4

What is the radius of the circle for the equation 2X^2 + 2Y^2 - 8X + 5Y + 10 = 0 after completing the square?

• 3/4

• 2

• 1/2

• 1