Exploring Adding and Subtracting Rational Expressions

The video tutorial explains how to write equations of circles given the center and radius. It covers the standard form of a circle equation and provides examples with both positive and negative centers. The tutorial also demonstrates how to find the radius using circumference and area, and how to determine the center and radius from a graph. Additionally, it explains the use of distance and midpoint formulas when given a center and a point on the circle, as well as how to find the center and radius from the endpoints of a diameter.

If the diameter of a circle is 18, what is the radius?

• 9

• 3

• 18

• 36

What is the standard form equation of a circle?

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r

• x^2 + y^2 = 2r

• (x - h)^2 + (y - k)^2 = r^2

What is the result of squaring the radius of a circle?

• The diameter of the circle

• The circumference of the circle

• The area of the circle

• The radius squared is used in the equation of the circle

If a circle has a center at (5/3, 2) and a radius of 2, what is the correct equation?

• (x - 5/3)^2 + (y - 2)^2 = 4

• (x + 5/3)^2 + (y + 2)^2 = 4

• (x - 5)^2 + (y - 3)^2 = 4

• (x - 2)^2 + (y - 5/3)^2 = 4

How do you find the radius if given the circumference of a circle?

• Divide the circumference by 2π

• Multiply the circumference by 2π

• Divide the circumference by π

• Square the circumference and divide by π

If a circle's center is at (3, -2) and its diameter is 10, what is the radius?

• 5

• 10

• 15

• 20

What formulas are necessary to write the equation of a circle given its center and a point on the circle?

• Slope and y-intercept formulas

• Area and circumference formulas

• Quadratic and linear equations

• Distance and midpoint formulas

If the center of a circle is (9, 10) and a point on the circle is (7, 4), what is the radius squared?

• 64

• 40

• 36

• 16

How do you find the center of a circle given the endpoints of its diameter?

• Add the x-values and y-values of the endpoints and divide by 2

• Subtract the x-values and y-values of the endpoints and divide by 2

• Divide the x-values and y-values of the endpoints by 2 without adding or subtracting

• Multiply the x-values and y-values of the endpoints and divide by 2

What is the equation of a circle with a center at (-12, 5) and a radius found from the diameter endpoints?

• (x - 12)^2 + (y - 5)^2 = 20

• (x + 12)^2 + (y - 5)^2 = 20

• (x - 12)^2 + (y + 5)^2 = 20

• (x + 12)^2 + (y + 5)^2 = 40