This video tutorial explains how to graph circles using standard equations, both with centers at the origin and translated centers. It covers converting non-standard circle equations to standard form by completing the square and demonstrates how to write circle equations given the center and radius. The tutorial provides step-by-step instructions for plotting points and connecting them to form a circle.

What is the standard equation of a circle with its center at the origin?

• x^2 + y^2 = 2r

• (x-h)^2 + (y-k)^2 = r^2

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

Tags

CCSS.HSG.GPE.A.1

If a circle's equation is x^2 + y^2 = 4, what is the radius?

• 16

• 2

• 8

• 4

Tags

CCSS.HSG.GPE.A.1

For the equation (x - 2)^2 + (y + 3)^2 = 16, where is the center located?

• (2, -3)

• (2, 3)

• (-2, 3)

• (-2, -3)

Tags

CCSS.HSG.GPE.A.1

How do you find the radius from the equation of a circle in standard form?

• Square root of the constant term

• The coefficient of x^2

• The difference between h and k

• Square root of the coefficient of x

Tags

CCSS.HSG.GPE.A.1

What is the first step in converting a circle's equation from non-standard to standard form?

• Move the constant to the other side

• Factor the equation

• Complete the square

• Group x and y terms together

Tags

CCSS.HSG.GPE.A.1

After completing the square for x^2 + 8x + 16, what is the factored form?

• (x - 4)^2

• (x + 2)^2

• x^2 + 4

• (x + 4)^2

Tags

CCSS.HSA-REI.B.4B

What is the center of a circle with the equation in standard form after completing the square: x^2 + 8x + y^2 - 6y = -21?

• (4, -3)

• (-4, 3)

• (-4, -3)

• (4, 3)

Tags

CCSS.HSG.GPE.A.1

Given a circle's center at (2, -5) and a radius of 3, what is the standard form of the equation?

• (x + 2)^2 + (y - 5)^2 = 9

• (x - 2)^2 + (y + 5)^2 = 9

• (x - 2)^2 + (y - 5)^2 = 9

• (x + 2)^2 + (y + 5)^2 = 9

Tags

CCSS.HSG.GPE.A.1

How do you adjust the equation x^2 + y^2 = r^2 to represent a circle's center at (h, k)?

• (x - h)^2 - (y - k)^2 = r^2

• x^2 - h + y^2 - k = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

Tags

CCSS.HSG.GPE.A.1

For the circle with center (-3, 7) and radius 6, what is the equation in standard form?

• (x - 3)^2 + (y - 7)^2 = 36

• (x - 3)^2 + (y + 7)^2 = 36

• (x + 3)^2 - (y - 7)^2 = 36

• (x + 3)^2 + (y - 7)^2 = 36

Tags

CCSS.HSG.GPE.A.1