Expanding the Equation of a Circle: Finding the Center and Radius

The video tutorial explains the general equation of a circle and demonstrates how to expand it using the grid or foil method. It covers rearranging the equation, substituting variables, and condensing terms to a single numerical value. The tutorial also explains how to calculate the center and radius of a circle from the expanded form and provides an example problem to illustrate these concepts.

What is the general form of the equation of a circle centered at (A, B)?

• (x - A)^2 - (y - B)^2 = R^2

• (x + A)^2 + (y + B)^2 = R^2

• (x + A)^2 - (y + B)^2 = R^2

• (x - A)^2 + (y - B)^2 = R^2

Which method is NOT mentioned for expanding the equation of a circle?

• Substitution method

• Grid method

• Long division method

• FOIL method

In the rearranged equation, what do the variables G and F replace?

• A and B

• G and H

• X and Y

• R and C

What does the term 'C' represent in the simplified equation?

• The center of the circle

• A single numerical value

• The radius of the circle

• The diameter of the circle

How can the radius of a circle be calculated from the expanded form?

• By finding the square root of G^2 + F^2 - C

• By multiplying G, F, and C

• By adding G and F

• By subtracting C from G and F

In the example provided, what is the center of the circle for the equation X^2 + Y^2 - 8X + 2Y = 13?

• (4, -1)

• (-4, 1)

• (4, 1)

• (-4, -1)

What is the calculated radius of the circle in the example?

• 1

• 2

• 3

• 4