Equations of Circles in Standard Form

The video tutorial covers the graphing of circles, focusing on the equation x-h squared plus y-k squared equals r squared. It explains how to find the center and radius of a circle from this equation and how to write a circle's equation given a description or graph. The tutorial uses Desmos for graphing and discusses the unit circle, Pythagorean theorem, and the effects of translations and radius changes on circle graphs. It concludes with an understanding of the standard form of circle equations.

What is the standard form equation for a circle?

• x - y = r^2

• x^2 + y^2 = r^2

• x^2 - y^2 = r

• x^2 + y^2 = r

What does the 'r' in the circle equation represent?

• Diameter

• Circumference

• Area

• Radius

How do you find the center of a circle in the equation x^2 + y^2 = 1?

• (0, 0)

• (-1, -1)

• (1, -1)

• (1, 1)

What is the radius of a unit circle?

• 2

• 0

• π

• 1

How does the equation change when the circle's center moves to (0, 2)?

• x^2 + (y+2)^2 = 1

• (x-2)^2 + y^2 = 1

• x^2 + y^2 = 2

• x^2 + (y-2)^2 = 1

What does the equation x^2 + (y-3)^2 = 1 indicate about the circle's center?

• Center at (0, -3)

• Center at (3, 0)

• Center at (0, 3)

• Center at (-3, 0)

What effect does changing the total value on the right side of the equation have?

• Translates the circle

• Changes the circle's color

• Stretches or shrinks the circle

• Rotates the circle

If the equation is x^2 + y^2 = 9, what is the radius of the circle?

• 3

• 18

• 6

• 9

In the equation x^2 + y^2 = 4, what does the 4 represent?

• An area of 4

• A circumference of 4

• A radius of 2

• Diameter of 4

Given the equation (x-6)^2 + (y+2)^2 = 25, what is the radius?

• 5

• 2

• 6

• 25