Exploring Equations of Circles

What is the standard form of a circle's equation?

• x^2 + y^2 = 2r

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r

If a circle's equation is x^2 + y^2 = 81, what is the radius of the circle?

• 8

• 18

• 81

• 9

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

• By multiplying the x and y coefficients

• By squaring the coefficients of x and y

• By taking the square root of the constant term

• From the terms (x-h) and (y-k) inside the squared terms

What is the center of a circle with the equation (x-1)^2 + y^2 = 25?

• (0, 1)

• (0, -1)

• (-1, 0)

• (1, 0)

Given a circle centered at (2, -4) with a radius of 4, what is the correct equation?

• (x-2)^2 + (y+4)^2 = 16

• (x+2)^2 + (y-4)^2 = 16

• (x-2)^2 + (y+4)^2 = 4

• (x+2)^2 + (y-4)^2 = 4

What does completing the square involve in terms of circle equations?

• Adding a constant to both sides of the equation

• Factoring the quadratic terms

• Isolating the y term on one side

• Dividing all terms by the coefficient of x^2

After completing the square for the equation x^2 - 6x + y^2 + 8y = 39, what is the new form?

• (x+3)^2 + (y+4)^2 = 64

• (x-3)^2 + (y-4)^2 = 64

• (x+3)^2 + (y-4)^2 = 64

• (x-3)^2 + (y+4)^2 = 64

What is the center of the circle if the equation is (x+1)^2 + (y-2)^2 = 16?

• (1, -2)

• (-1, -2)

• (-1, 2)

• (1, 2)

How do you find the radius from the equation (x-3)^2 + (y+2)^2 = 9?

• 18

• 6

• 9

• 3

From a graph, if the center of a circle is at (2, 0) and touches the x-axis at (4, 0), what is the radius?

• 8

• 1

• 4

• 2