Equations of Circles and Completing the Square

This video tutorial covers the equations of circles, including the standard equation, graphing techniques, and completing the square. It explains how to find the center and radius of a circle, graph circles, and solve practice problems. The tutorial provides step-by-step instructions and examples to help students understand and apply these concepts effectively.

What are the coordinates of the center of a circle in the equation (x - h)^2 + (y - k)^2 = r^2?

• (0, 0)

• (r, r)

• (-h, -k)

• (h, k)

How do you find the center of a circle given its equation in standard form?

• By calculating the diameter

• By identifying the h and k values

• By determining the area

• By finding the slope

What is the standard form equation of a circle?

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

• (h - x)^2 + (k - y)^2 = r^2

• xh^2 + yk^2 = r

If the diameter of a circle is 8 units, what is its radius?

• 4 units

• 16 units

• 8 units

• 2 units

If a circle's equation is x^2 + y^2 = 64, what is the radius of the circle?

• 32

• 64

• 16

• 8

What does the equation x^2 + y^2 = r^2 indicate about the circle's center?

• The center is at (r, r)

• The center is at (0, 0)

• The center is undefined

• The center is at (1, 1)

What does the radius equal if the equation of a circle is x^2 + y^2 = 81?

• 9

• 40.5

• 81

• 18

If the equation of a circle is (x - 3)^2 + (y + 2)^2 = 16, what is the center of the circle?

• (3, -2)

• (-3, 2)

• (3, 2)

• (-3, -2)

When given a circle's equation, how can you determine its radius?

• By adding the x and y coefficients

• By finding the difference between h and k

• By doubling the h and k values

• By taking the square root of the right side of the equation

How do you rearrange an equation to find the standard form of a circle's equation?

• Multiply each term by the radius

• Group variables, use placeholders, and square the middle term

• Subtract h and k from both sides

• Divide each term by 2