Understanding Equations of Circles

What is the standard form of a circle's equation with center (H, K) and radius R?

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 = (H + K)^2

• (X + H)^2 + (Y + K)^2 = R^2

• X^2 + Y^2 = R^2

If a circle has a center at (0, 0) and a radius of 8, what is the equation of the circle?

• X^2 + Y^2 = 64

• X^2 + Y^2 = 8

• (X - 8)^2 + (Y - 8)^2 = 64

• (X + 8)^2 + (Y + 8)^2 = 64

How do you find the radius if you are given the diameter of a circle?

• Multiply the diameter by 2

• Take the square root of the diameter

• Square the diameter

• Divide the diameter by 2

What formula is used to find the distance between two points, which can also be used to find the radius of a circle?

• Midpoint formula

• Slope formula

• Quadratic formula

• Distance formula

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

• (X + 3)^2 + (Y + 4)^2 = 16

• (X - 3)^2 + (Y - 4)^2 = 16

• (X - 3)^2 + (Y + 4)^2 = 16

• (X + 3)^2 + (Y - 4)^2 = 16

When graphing a circle with the equation X^2 + Y^2 = 16, what is the radius?

• 8

• 4

• 16

• 2

If a circle's equation is (X - 2)^2 + (Y - 1)^2 = 9, what is the center of the circle?

• (-2, 1)

• (-2, -1)

• (2, 1)

• (2, -1)

How do you determine the center of a circle from three given points?

• Use the point closest to the origin

• Find the point equidistant from all three

• Use the point farthest from the others

• Find the midpoint of any two points

What is the equation of a circle with center (-1, 2) and radius 1?

• (X - 1)^2 + (Y + 2)^2 = 1

• (X - 1)^2 + (Y - 2)^2 = 1

• (X + 1)^2 + (Y + 2)^2 = 1

• (X + 1)^2 + (Y - 2)^2 = 1

What is the first step in writing the equation of a circle when given three points?

• Calculate the radius

• Identify the center

• Plot the points on a graph

• Find the midpoint of the diameter