Circle Equations and Properties

This lesson teaches how to find the center and radius of a circle by examining its equation. It begins with a review of the graph of a circle, highlighting the center and radius. The standard form of a circle's equation is introduced, explaining the significance of each component, including h, k, and r. Two examples demonstrate how to rewrite equations into standard form, identifying the center and radius from the equation. The lesson concludes with a summary of the process for determining these circle properties from the equation.

What is the center of a circle?

• A line from the center to the edge

• The diameter of the circle

• A point around which the circle is drawn

• The circumference of the circle

What does the 'r' represent in the standard form equation of a circle?

• The diameter

• The circumference

• The radius

• The center

In the equation (x - h)^2 + (y - k)^2 = r^2, what do 'h' and 'k' represent?

• The diameter

• The circumference

• The center coordinates

• The radius

Why must the terms in the standard form equation be written as subtraction?

• To simplify the equation

• To ensure the equation is balanced

• To find the diameter

• To correctly identify the center

In the equation x^2 + y^2 = 81, what is the radius?

• 27

• 3

• 9

• 81

How can you rewrite x + 6 in the standard form?

• x + 6

• x + (-6)

• x - (-6)

• x - 6

What is the center of the circle for the equation x^2 + (y - 3)^2 = 30?

• (3, 0)

• (0, 3)

• (-3, 0)

• (0, -3)

How can you express 30 as a squared number in the equation x^2 + (y - 3)^2 = 30?

• 30^2

• sqrt(30)^2

• 5^2

• 15^2

What is the radius of the circle for the equation x^2 + (y - 3)^2 = 30?

• sqrt(30)

• 3

• 30

• 15

What is the importance of rewriting an equation in standard form?

• To identify the center and radius

• To determine the circumference

• To find the diameter

• To calculate the area