Exploring Equations of Circles

This video tutorial covers how to write equations of circles when given the center and either the area or the circumference. It explains the process of finding the radius using the area formula (A = πr²) and the circumference formula (C = 2πr). The tutorial includes two examples: one using the area to find the radius and write the circle equation, and another using the circumference. The video emphasizes understanding the formulas and solving for the radius to complete the circle equation.

What is needed to write the equation of a circle?

• Radius and area

• Center and radius

• Diameter and circumference

• Center and diameter

How do you find the radius from the area of a circle?

• Multiply the area by the diameter

• Square the area and divide by pi

• Divide the area by pi and square root the result

• Multiply the area by pi

What is the area formula of a circle?

• A = 2r^2

• A = πr^2

• A = 2πr

• A = πr

What step follows after finding the radius when writing the equation of a circle?

• Use the radius and center to write the equation

• Divide the radius by π

• Multiply the radius by 2

• Square the radius

What is the correct equation of a circle given its center (-15, 3) and radius as the square root of 2?

• x + 15 + y + 3 = 2

• x - 15^2 + y + 3^2 = 2

• x + 15^2 + y - 3^2 = 2

• x - 15^2 + y - 3^2 = 2

How is the circumference formula of a circle expressed?

• C = πr^2

• C = 2πr

• C = πd

• C = 2r

What is the first step in finding the radius given the circumference?

• Set up an equation using the circumference formula

• Square the circumference

• Divide the circumference by π

• Multiply the circumference by 2

What operation is performed to isolate r in the equation C = 2πr?

• Multiplication

• Subtraction

• Division

• Addition

Given a circle's center and circumference, what is the next step after finding the radius?

• Double the radius

• Write the equation using the center and radius

• Find the area of the circle

• Calculate the diameter

How do you find the radius when given the circumference of 8π?

• r = 8/π

• r = 4

• r = 4π

• r = 8π