Understanding Equations of Circles

What is the equation of a circle centered at the origin with radius R?

• x^2 + y^2 = R^2

• x^2 + y^2 = 2R^2

• x^2 + y^2 = R

• x^2 + y^2 = 2R

How does the equation of a circle change when the center is at (h, k)?

• (x - h)^2 + (y - k)^2 = R^2

• (x + h)^2 + (y + k)^2 = R^2

• (x + h)^2 + (y - k)^2 = R^2

• (x - h)^2 + (y + k)^2 = R^2

If a circle has a center at (3, -2) and a point on the circle at (6, 2), what is the radius?

• 6

• 3

• 4

• 5

Given the equation (x + 2)^2 + (y - 3)^2 = 16, what is the center of the circle?

• (-2, 3)

• (2, -3)

• (-2, -3)

• (2, 3)

What is the radius of a circle with the equation (x - 4)^2 + (y + 5)^2 = 49?

• 7

• 5

• 6

• 8

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

• Square R^2

• Halve R^2

• Take the square root of R^2

• Double R^2

If the center of a circle is at (-3, 4) and the radius is 5, what is the equation of the circle?

• (x + 3)^2 + (y + 4)^2 = 25

• (x - 3)^2 + (y + 4)^2 = 25

• (x - 3)^2 + (y - 4)^2 = 25

• (x + 3)^2 + (y - 4)^2 = 25

What is the center of a circle with the equation (x - 1)^2 + (y + 2)^2 = 36?

• (1, -2)

• (-1, -2)

• (1, 2)

• (-1, 2)

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

• By subtracting the constants in (x - h) and (y - k)

• By taking the opposite signs of the constants in (x - h) and (y - k)

• By multiplying the constants in (x - h) and (y - k)

• By adding the constants in (x - h) and (y - k)

What is the radius of a circle with the equation (x + 5)^2 + (y - 7)^2 = 64?

• 8

• 7

• 6

• 9