Circle Equations and Properties

The video tutorial explains how to work with circles on a coordinate plane using two main formulas: the distance formula to find the radius and the equation of a circle. It demonstrates how to apply these formulas with given center coordinates and radius, and how to calculate the radius when a point on the circle is known. The tutorial also covers graphing a circle by identifying the center and radius, and provides tips for drawing circles accurately.

What is the purpose of using the distance formula in relation to circles on a coordinate plane?

• To calculate the circumference of the circle

• To identify the center of the circle

• To determine the radius of the circle

• To find the diameter of the circle

Which of the following represents the general form of the equation of a circle?

• X^2 + Y^2 = 2R

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 = R^2

• (X + H)^2 + (Y + K)^2 = R

If a circle has a center at (4, -3) and a radius of 3, what is the equation of the circle?

• (X - 4)^2 + (Y + 3)^2 = 9

• (X + 4)^2 + (Y - 3)^2 = 9

• (X + 4)^2 + (Y + 3)^2 = 9

• (X - 4)^2 + (Y - 3)^2 = 9

Given a circle with center (-6, 3) and passing through the point (-2, 6), what is the radius of the circle?

• 6

• 5

• 4

• 3

What is the equation of a circle with center (-6, 3) and radius 5?

• (X + 6)^2 + (Y - 3)^2 = 25

• (X - 6)^2 + (Y - 3)^2 = 25

• (X - 6)^2 + (Y + 3)^2 = 25

• (X + 6)^2 + (Y + 3)^2 = 25

When graphing a circle, what two key pieces of information are needed?

• The center and the diameter

• The area and the circumference

• The center and the radius

• The diameter and the circumference

In the equation (X + 2)^2 + (Y - 3)^2 = 9, what is the center of the circle?

• (2, -3)

• (-2, -3)

• (-2, 3)

• (2, 3)

How can you determine the radius from the equation (X + 2)^2 + (Y - 3)^2 = 9?

• The radius is 9

• The radius is 3

• The radius is 1

• The radius is 2

What tool can help you draw a perfect circle by hand?

• A compass

• A set square

• A ruler

• A protractor

Which software is mentioned as useful for drawing circles digitally?

• Sketchbook

• Photoshop

• Paint

• Illustrator