Writing the Equation of a Circle in Standard Form

The video tutorial explains the standard form of a circle's equation: (X - H)^2 + (Y - K)^2 = R^2. It reviews the components of a circle, including the center (H, K) and the radius R. The tutorial provides an example where the center is at (-2, 0) and the radius is 16, demonstrating how to substitute these values into the equation to find the circle's equation.

What does R represent in the circle's equation?

• Radius of the circle

• Area of the circle

• Circumference of the circle

• Diameter of the circle

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

• Length of the radius

• Coordinates of any point on the circle

• Slope of the diameter

• Coordinates of the circle's center

How is the standard form equation of a circle derived?

• By calculating the area of the circle

• Through the circle's circumference formula

• From the Pythagorean theorem

• By squaring the circle's diameter

If a circle's center is at (-2, 0), what is the correct substitution for h and k in the equation?

• x - (-2) and y - 0

• x + 2 and y + 0

• x - 2 and y - 0

• x + 2 and y - 0

What is the value of r^2 if the radius of the circle is 16?

• 256

• 128

• 32

• 64

When simplifying x - (-2)^2 + y - 0^2 = 16^2, what does the equation become?

• (x + 2)^2 + y^2 = 256

• x^2 + 4 + y^2 = 256

• (x + 2)^2 + y^2 = 16

• (x - 2)^2 + y^2 = 256