Given the equation of a circle find the center and radius

The video tutorial explains how to graph a circle given its equation in standard form. It begins by identifying the center of the circle and then discusses the concept of R-squared. The tutorial demonstrates how to simplify the equation by dividing out coefficients to find the radius. Finally, it shows how to graph the circle using the calculated center and radius.

What is the center of the circle given the equation 3x^2 + 3y^2 = 12?

• (3, 3)

• (0, 0)

• (1, 1)

• (2, 2)

How can you simplify the equation 3x^2 + 3y^2 = 12 to find the radius?

• Add 3 to both sides

• Multiply both sides by 3

• Subtract 3 from both sides

• Divide both sides by 3

What is the radius of the circle after simplifying the equation 3x^2 + 3y^2 = 12?

• 1

• 2

• 4

• 3

When graphing a circle, why is it important to isolate the coefficients in the equation?

• To find the diameter

• To determine the color of the graph

• To change the center of the circle

• To accurately find the radius

What does the radius represent in the context of a circle's graph?

• The width of the circle

• The distance from the center to any point on the circle

• The height of the circle

• The circumference of the circle