Exploring the Equation of a Circle

What is the general formula for the equation of a circle?

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r

• x^2 + y^2 + r^2 = 0

How do you find the center of a circle on a graph?

• By calculating the average of all the x and y coordinates on the circle

• By drawing lines from the highest and widest points of the circle to find where they intersect

• By finding the midpoint of the diameter

• By locating the point where the circle touches the x-axis

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

• (x - 4)^2 + (y + 5)^2 = 9

• (x + 4)^2 + (y - 5)^2 = 9

• (x - 4)^2 + (y + 5)^2 = 3

• (x + 4)^2 + (y - 5)^2 = 3

If a circle's equation is (x - 3)^2 + (y + 2)^2 = 25, what is the radius?

• 25

• √25

• 5

• 50

If the diameter of a circle is 10, what is the radius?

• 15

• 10

• 5

• 20

How do you graph a circle given its equation?

• By using a compass set to the radius length from the center

• By drawing a square and inscribing the circle within it

• By plotting points randomly within the circle

• By identifying the center and radius and then drawing the circle

What is the center of a circle with the equation (x + 2)^2 + (y - 3)^2 = 16?

• (2, -3)

• (-2, 3)

• (-2, -3)

• (2, 3)

If the equation of a circle is x^2 + y^2 = 36, where is the center located?

• (0, 0)

• (6, 6)

• (36, 36)

• (-6, -6)

What does completing the square allow you to find in a circle's equation?

• The area of the circle

• The circle's diameter

• The circle's circumference

• The center and radius of the circle

When completing the square for the equation x^2 + 6x + y^2 - 4y = 12, what is the new form of the equation?

• (x + 3)^2 + (y - 2)^2 = 25

• (x - 3)^2 + (y - 2)^2 = 13

• (x - 3)^2 + (y + 2)^2 = 25

• (x + 3)^2 + (y + 2)^2 = 13