Circle Geometry Concepts

The video tutorial covers writing equations of circles, starting with an introduction to the standard form. It provides examples using given centers and radii, and explains how to use circumference and area to find circle equations. The tutorial also demonstrates finding equations from graphs and using the distance formula to calculate the radius. It concludes with a discussion on finding midpoints and radii, and offers practice problems for students.

What is the standard form of the equation of a circle?

• (x + h)^2 + (y + k)^2 = r^2

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

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

• (x - 5)^2 + (y - 3)^2 = 4

• (x + 5)^2 + (y + 3)^2 = 2

• (x + 5)^2 + (y + 3)^2 = 4

• (x - 5)^2 + (y - 3)^2 = 2

How do you find the radius if the diameter is given as 18?

• Subtract 2 from the diameter

• Add 2 to the diameter

• Multiply the diameter by 2

• Divide the diameter by 2

Given a circumference of 17π, what is the radius of the circle?

• 8.5

• 17

• 34

• 4.25

If the area of a circle is 361π, what is the radius?

• 19

• 361

• 180.5

• 9.5

How can you find the center of a circle from a graph?

• By finding the midpoint of the diameter

• By measuring the radius

• By calculating the area

• By using the circumference

What formula is used to find the radius when given a point on the circle?

• Distance formula

• Midpoint formula

• Slope formula

• Area formula

What is the radius if the distance between the center (1, -5) and a point (-7, -13) is calculated?

• 64

• √128

• 128

• √64

If the center of a circle is (-2, 0) and a point on the circle is (-9, -4), what is the radius?

• 49

• √49

• 65

• √65

How do you find the center of a circle using two points on the circle?

• Use the area formula

• Use the midpoint formula

• Use the distance formula

• Use the slope formula