Understanding Circle Equations

The video tutorial explains how to determine the center and radius of a circle from its equation in standard form. It provides four examples, each demonstrating different scenarios such as dealing with negative coordinates and fractions. The tutorial emphasizes recognizing the standard form and using algebraic manipulation to find the center and radius.

What is the standard form of a circle's equation?

• (x + h)^2 + (y + k)^2 = r^2

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

In the equation (x - 3)^2 + (y + 5)^2 = 81, what is the radius of the circle?

• 3

• 5

• 9

• 81

For the equation (x + 7)^2 + (y - 1)^2 = 72, what is the x-coordinate of the center?

• -1

• 1

• 7

• -7

How do you simplify the square root of 72?

• 6√2

• 7√3

• 9√2

• 8√3

In the equation (x + 2/3)^2 + (y - 4/9)^2 = 2536, what is the y-coordinate of the center?

• -2/3

• 2/3

• -4/9

• 4/9

What is the radius of the circle if r^2 = 2536?

• 6/5

• 25/36

• 5/6

• 36/25

In the equation (x + 4/5)^2 + (y + 7/9)^2 = 48/81, what is the x-coordinate of the center?

• 4/5

• -7/9

• -4/5

• 7/9

How do you simplify the square root of 48?

• 6√2

• 7√3

• 5√2

• 4√3

What is the radius of the circle if r^2 = 48/81?

• 4√3/9

• 7√3/9

• 5√2/9

• 6√2/9

What is the y-coordinate of the center in the equation (x + 4/5)^2 + (y + 7/9)^2 = 48/81?

• -7/9

• 4/5

• 7/9

• -4/5