Exploring Equations of Circles

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

• (h, k)

• (0, 0)

• (r, r)

• (x, y)

How is the radius represented in the circle's standard equation?

• h + k

• x - y

• sqrt(h^2 + k^2)

• r^2

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

• x^2 + y^2 = r^2

• h^2 + k^2 = r^2

• (x - h)^2 + (y - k)^2 = r

• (x - h)^2 + (y - k)^2 = r^2

If a circle's equation is x^2 + y^2 = 9, what is the radius of the circle?

• 3

• 81

• 9

• 18

What does a double negative in a circle's equation convert to?

• Remains as a negative

• None of the above

• Is eliminated

• Becomes a positive

If the center of a circle is at (1, -2) and the radius is 4, what is the correct form of the circle's equation?

• (x + 1)^2 + (y - 2)^2 = 4

• (x - 1)^2 + (y + 2)^2 = 4

• (x + 1)^2 + (y - 2)^2 = 16

• (x - 1)^2 + (y + 2)^2 = 16

How do you find the radius if you're given a point on the circle and the center?

• Multiply the coordinates

• Subtract the center from the point

• Use the midpoint formula

• Apply the distance formula

What indicates a point lies outside the circle?

• The result is less than r^2

• None of the above

• The result is greater than r^2

• The result is equal to r^2

What indicates a point lies on the circle?

• The result is less than r^2

• The result is zero

• The result is greater than r^2

• The result equals r^2

If a point inside a circle gives a result less than r^2 when plugged into the equation, what does it indicate?

• The point is on the circle

• The point is inside the circle

• The equation is incorrect

• The point is outside the circle