Circle Geometry and Equations

The video tutorial explains the equation of a circle, x^2 + y^2 = R^2, and how it represents a circle with a center at the origin and a radius R. It provides examples of different circle equations, demonstrates how to rewrite equations to find the radius, and explains how to draw circles using compasses. The tutorial also covers the reverse process of finding equations from given circle graphs and calculating circle properties like radius, diameter, and area. Advanced examples include simplifying square roots and handling mixed numbers. The video concludes with final questions and encourages viewers to practice with provided exam questions.

What is the general form of the equation of a circle centered at the origin?

• x^2 + y^2 = r

• x + y = r^2

• x^2 + y^2 = r^2

• x^2 + y = r^2

If a circle has the equation x^2 + y^2 = 25, what is its radius?

• 5

• 10

• 25

• 50

How would you rewrite the equation x^2 + y^2 = 49 to find the radius?

• x^2 + y^2 = 49^2

• x^2 + y^2 = 24.5^2

• x^2 + y^2 = 7^2

• x^2 + y^2 = 14^2

What tool is essential for drawing a circle with a given radius on a graph?

• Set square

• Ruler

• Protractor

• Pair of compasses

If a circle graph crosses the axes at 6 and -6, what is the radius?

• 18

• 12

• 6

• 3

Given the equation x^2 + y^2 = 81, what is the diameter of the circle?

• 162

• 81

• 18

• 9

What is the area of a circle with a radius of 4?

• 8π

• 64π

• 4π

• 16π

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

• 32

• 16

• 8

• 4

What is the diameter of a circle with the equation x^2 + y^2 = 100?

• 50

• 20

• 100

• 10

How do you express the radius of a circle with the equation x^2 + y^2 = 121?

• √121

• 121

• 22

• 11