Graphing and Writing Equations of Circles in Standard Form

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