Equations of Circles and Completing the Square

What are the coordinates of a circle's center in the XY plane?

• (x, y)

• (0, 0)

• (h, k)

• (r, r)

What is the standard form equation of a circle?

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r

• x^2 + y^2 + r^2 = 0

What does R squared represent in the circle's equation?

• Diameter of the circle

• Radius of the circle squared

• Circumference of the circle

• Area of the circle

What does the distance formula help to find in the context of circles?

• The circle's circumference

• The area of the circle

• The circle's diameter

• The length of the radius

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

• By squaring the radius

• By finding the square root of R squared

• By using the coefficients of x and y

• By completing the square

How can you graph a circle given its equation?

• By drawing a square around the center

• By calculating the center and radius

• By using the Pythagorean theorem

• By plotting points randomly

A point is inside the circle if the calculated R squared is:

• Less than the circle's R squared

• Greater than the circle's R squared

• Twice the circle's R squared

• Equal to the circle's R squared

If a point's calculated R squared is greater than the circle's R squared, the point is:

• At the center of the circle

• On the circle

• Inside the circle

• Outside the circle

What is the purpose of completing the square in the context of a circle's equation?

• To find the circle's diameter

• To convert the general form to standard form

• To calculate the area of the circle

• To determine the circle's circumference

What is the result of completing the square for a circle's equation?

• Calculating the circle's area

• Determining the circle's diameter

• Measuring the circle's circumference

• Finding the circle's center and radius