Finding the Center and Radius of a Circle

What defines a circle in a geometric sense?

• A shape with equal angles

• A set of points equidistant from a fixed point

• A shape with four equal sides

• A set of points forming a square

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

• A hyperbola

• A parabola

• An ellipse

• A circle

What is the radius of a circle with the equation x^2 + y^2 = 9?

• 9

• 18

• 6

• 3

How is the center of a circle shifted on the coordinate plane?

• By changing the equation's constants

• By subtracting from the x and y coordinates

• By multiplying the radius

• By adding to the x and y coordinates

What is the standard form equation of a circle centered at the origin with radius r?

• x^2 - y^2 = r^2

• (x-h)^2 + (y-k)^2 = r^2

• x^2 + y^2 = r^2

• x^2 + y^2 = r

In the equation (x-h)^2 + (y-k)^2 = r^2, what do h and k represent?

• The center of the circle

• The diameter of the circle

• The radius of the circle

• The circumference of the circle

What does completing the square help to identify in a circle's equation?

• The circle's area

• The circle's center and radius

• The circle's circumference

• The circle's diameter

How do you complete the square for the equation x^2 + bx?

• Divide by b

• Add (b/2)^2

• Subtract (b/2)^2

• Multiply by b

What is the effect of factoring out a coefficient before completing the square?

• It allows for the creation of a perfect square trinomial

• It identifies the circle's center

• It changes the radius

• It simplifies the equation

When completing the square, what do you do after adding a constant inside the parentheses?

• Divide the constant by the coefficient outside the parentheses

• Multiply the constant by the coefficient outside the parentheses

• Add the same constant to both sides

• Subtract the same constant from both sides