Equations of Circles: Center and Radius Identification

This video tutorial by Kirk Weiler covers the equations of circles in geometry. It begins with a review of line equations to set the foundation for understanding circle equations. The tutorial explains the basic equation of a circle centered at the origin and provides examples to illustrate the concept. It then explores circles not centered at the origin, deriving the general equation of a circle. The video concludes with a summary of the key points discussed.

What is not an equation of a circle?

• x^2 + y^2 = 100

• Area = πr^2

• x - y = 0

• x^2 + y^2 = r^2

What does the equation x^2 + y^2 = r^2 represent?

• A parabola

• A circle centered at the origin

• A line

• An ellipse

How do you find the radius from the equation x^2 + y^2 = 100?

• Square root of 100

• 10

• 100

• 10 squared

What is the radius of a circle whose equation is x^2 + y^2 = 36?

• Square root of 36

• 18

• 36

• 6

Which equation represents a circle with a radius of 8?

• x^2 + y^2 = 64

• x^2 + y^2 = 16

• x^2 + y^2 = 8

• (x - 8)^2 + (y - 8)^2 = 64

How do you determine if a point lies on a circle with the equation x^2 + y^2 = r^2?

• Check if the point's coordinates are equal

• Substitute the point into the equation and see if it equals r^2

• Ensure the point's coordinates add up to r

• Substitute the point into the equation and see if it equals r

What is the center of a circle with the equation (x - 4)^2 + (y - 2)^2 = 25?

• (25, 25)

• (-4, -2)

• (2, 4)

• (4, 2)

For a circle not centered at the origin with equation (x - 3)^2 + (y + 2)^2 = 49, what is the radius?

• 49

• 14

• 7

• Square root of 49

What is the general equation for a circle not centered at the origin?

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

• (x - a)^2 + (y - b)^2 = r^2

• x/a + y/b = 1

If a circle's equation is (x + 5)^2 + (y - 5)^2 = 25, what is the center?

• (0, 0)

• (25, 25)

• (-5, 5)

• (5, -5)