Find the center and radius of a circle by completing the square

The video tutorial explains the process of completing the square to find the center and radius of a circle. It begins with rearranging terms and emphasizes the importance of grouping X's and Y's. The instructor demonstrates how to complete the square for both X and Y terms, using the formula B/2 squared. The tutorial concludes with factoring the binomial squares and calculating the circle's center and radius.

Why is it important to rearrange the terms with X's and Y's together when completing the square?

• To facilitate completing the square

• To ensure the equation is balanced

• To make it easier to factor

• To simplify the equation

What is the first step in completing the square for a term like X^2 - 4X?

• Add 4 to both sides

• Subtract 4 from both sides

• Divide the linear coefficient by 2 and square it

• Multiply the linear coefficient by 2

How do you determine the value to add inside the parentheses when completing the square?

• Add the linear coefficient to the constant term

• Divide the linear coefficient by 2 and square it

• Multiply the linear coefficient by 2

• Square the constant term

What is the result of factoring the completed square X^2 - 4X + 4?

• (X + 4)^2

• (X - 2)^2

• (X + 2)^2

• (X - 4)^2

What is the center of the circle given by the equation (X - 2)^2 + (Y + 3)^2 = 15?

• (-2, -3)

• (2, 3)

• (-2, 3)

• (2, -3)