Exploring Equations of Circles

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

• (x, y)

• (0, 0)

• (h, k)

• (r, r)

How is the radius represented in the standard form equation of a circle?

• x

• r

• h

• k

If a circle's equation is (x - h)^2 + (y - k)^2 = r^2, what does 'r' stand for?

• The area of the circle

• The radius of the circle

• The circumference of the circle

• The diameter of the circle

What is the correct way to express a circle's center in its equation?

• Using (a, b) coordinates

• Using (h, k) coordinates

• Using (x, y) coordinates

• Using (r, r) values

What is the standard form equation of a circle with center (2, -3) and radius 6?

• (x + 2)^2 + (y + 3)^2 = 6

• (x - 2)^2 + (y + 3)^2 = 36

• (x + 2)^2 + (y - 3)^2 = 36

• (x - 2)^2 + (y - 3)^2 = 6

For a circle centered at the origin with radius 10, what is the equation?

• x^2 + y^2 = 10

• x^2 + y^2 = 100

• x + y = 100

• x + y = 10

How do you find the radius if it's not directly given?

• By squaring the diameter

• By doubling the circumference

• By using the distance formula

• By using the midpoint formula

What is the equation of a circle with center at (-2, 6) and a point on the circle at (-6, 1)?

• (x - 2)^2 + (y + 6)^2 = 41

• (x - 2)^2 + (y + 6)^2 = sqrt(41)

• (x + 2)^2 + (y - 6)^2 = 41

• (x + 2)^2 + (y - 6)^2 = sqrt(41)

How do you graph a circle given its equation?

• By drawing a square with side length equal to the diameter

• By using a compass set to the radius length

• By calculating the diameter and drawing around the center

• By plotting the center and radius on a coordinate plane

What does the equation x^2 + y^2 = 25 represent?

• A circle centered at (0, 0) with radius 5

• A circle centered at (5, 5) with radius 5

• A circle centered at (5, 5) with radius 25

• A circle centered at (0, 0) with radius 25