Circle Equations and Properties

This video tutorial covers the topic of circle equations for 11th-grade students, focusing on conic sections. It explains three types of circle equations: one with the center at the origin, another with the center at any point (a,b), and the general form. The tutorial provides formulas for each type and demonstrates how to find the center and radius from the general form. It includes practice problems to reinforce understanding and offers solutions to multiple-choice questions.

What is the equation of a circle with its center at the origin and radius 5?

• x² + y² = 20

• x² + y² = 10

• x² + y² = 5

• x² + y² = 25

Tags

CCSS.HSG.GPE.A.1

What is the general form of a circle's equation when the center is at the origin?

• x² + y² = r²

• x² + y² + Ax + By = 0

• (x + a)² + (y + b)² = r²

• (x - a)² + (y - b)² = r²

Tags

CCSS.HSG.GPE.A.1

If a circle's center is at (a, b) and its radius is r, what is the general form of its equation?

• (x - a)² + (y - b)² = r²

• x² + y² = r²

• (x + a)² + (y + b)² = r²

• x² + y² + ax + by = r²

Tags

CCSS.HSG.GPE.A.1

How do you find the center of a circle given by the equation x² + y² + Ax + By + C = 0?

• (A/2, B/2)

• (A, B)

• (-A/2, -B/2)

• (-A, -B)

Tags

CCSS.HSG.GPE.A.1

In the equation x² + y² + Ax + By + C = 0, what does the term -A/2 represent?

• The radius

• The diameter

• The y-coordinate of the center

• The x-coordinate of the center

Tags

CCSS.HSG.GPE.A.1

What is the radius of a circle with the equation x² + y² = 36?

• 6

• 12

• 36

• 18

Tags

CCSS.HSG.GPE.A.1

For the equation 5x² + 5y² = 75, what is the radius of the circle?

• 5

• 15

• √15

• √75

Tags

CCSS.HSG.GPE.A.1

How do you transform the equation x² + y² - 6 = 0 to find the radius?

• Set x² + y² = -6

• Set x² + y² = 6

• Set x² + y² = 0

• Set x² + y² = 12

Tags

CCSS.HSG.GPE.A.1

What is the radius of a circle with the equation x² + y² = 15?

• √15

• 15

• 30

• √30

Tags

CCSS.HSG.GPE.A.1

What is the center of the circle given by the equation x² + y² - 4x + 2y - 10 = 0?

• (-4, 2)

• (2, -1)

• (-2, 1)

• (4, -2)

Tags

CCSS.HSG.GPE.A.1