Completing the Square and Circle Equations

The video tutorial explains how to find the center and radius of a circle by writing its equation in standard form. It involves clearing parentheses, completing the square for both x and y terms, and factoring to determine the center and radius. The center is found to be at (-2, 4) and the radius is 5.

What is the first step in writing the equation of a circle in standard form?

• Completing the square

• Identifying the center

• Clearing the parentheses

• Finding the radius

When completing the square for x^2 + 4x, what value is added to both sides of the equation?

• 16

• 2

• 4

• 8

What is the result of completing the square for y^2 - 8y?

• (y - 4)^2

• (y + 8)^2

• (y + 4)^2

• (y - 8)^2

What is the center of the circle after factoring the completed squares?

• (2, -4)

• (-4, 2)

• (4, -2)

• (-2, 4)

If r^2 equals 25, what is the radius of the circle?

• 6

• 4

• 3

• 5