Exploring the Equation of a Circle

What is the standard equation of a circle?

• (x + h)^2 + (y + k)^2 = r

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = 2r

What represents the center of a circle in its standard equation?

• (r, r)

• (x, y)

• (h, k)

• (0, 0)

How do you determine the radius in the equation of a circle?

• The square root of r

• The sum of x and y coordinates

• The difference between h and k

• Distance from the center to any point on the circle

If the center of a circle is at (0, 0), what is the equation if the radius is 3?

• (x - 3)^2 + (y - 3)^2 = 9

• (x - 0)^2 + (y - 0)^2 = 3^2

• x^2 + y^2 = 3

• x^2 + y^2 = 9

For a circle with center (2, 2) and radius 4, what is the correct equation?

• (x - 4)^2 + (y - 4)^2 = 2^2

• (x + 2)^2 + (y + 2)^2 = 16

• x^2 + y^2 = 4

• (x - 2)^2 + (y - 2)^2 = 16

Given the equation x^2 + y^2 = 4, what is the radius of the circle?

• 8

• 4

• 2

• 16

If the equation of a circle is (x - 5)^2 + (y + 8)^2 = 36, what is the center?

• (-5, 8)

• (5, -8)

• (-5, -8)

• (5, 8)

How do you find the radius from the equation (x - h)^2 + (y - k)^2 = r^2?

• Add h and k

• Multiply h and k

• Take the square root of r^2

• Subtract h from k

What does a positive number in the equation of a circle indicate about the coordinate?

• The coordinate is positive

• The coordinate is negative

• The coordinate is zero

• The coordinate is doubled

In the equation (x + 3)^2 + (y - 2)^2 = 9, what is the x-coordinate of the center?

• 3

• -3

• -2

• 2