Exploring the Equation of a Circle

What theorem is essential for understanding the consistent distance in a circle?

• Euclidean Theorem

• Pythagorean Theorem

• Thales' Theorem

• Fermat's Last Theorem

What does the center of a circle at (3,2) indicate in terms of movement from the origin?

• Left 3, down 2

• Right 3, up 2

• Left 2, up 3

• Right 2, down 3

How is the radius of a circle expressed using the distance formula?

• Radius = (x - 3)^2 + (y - 2)^2

• Radius = sqrt((x - 3)^2 + (y - 2)^2)

• Radius = sqrt(x^2 + y^2)

• Radius = x^2 + y^2

What pattern is recognized in the equation of a circle regarding the center's coordinates?

• The coordinates are directly used.

• The coordinates are squared.

• The signs of the coordinates are reversed.

• The coordinates are multiplied by two.

If a circle's center is at (-3, -2), how is it represented in the equation?

• x + 3 and y + 2

• x - 3 and y - 2

• x + 2 and y + 3

• x - 2 and y - 3

How do you determine the center of a circle from its equation?

• By doubling the radius

• By adding 1 to both x and y coordinates

• By taking the square root of the radius

• By reversing the signs of x and y in the equation

What is the radius of a circle with an equation where r squared equals 16?

• 16

• 32

• 8

• 4

What is the first step in sketching the graph of a circle?

• Calculating the circumference

• Drawing the radius

• Determining the diameter

• Identifying the center

How can the equation of a circle help in graphing it?

• It provides the slope of the circle.

• It indicates the center and radius of the circle.

• It determines the circle's tangents.

• It shows the intercepts on the axes.

What does the square root of the radius squared represent?

• The area of the circle

• The diameter of the circle

• The actual radius of the circle

• The circumference of the circle