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

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

• 16

• 2

• 8

• 4

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

• (2, -3)

• (2, 3)

• (-2, 3)

• (-2, -3)

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

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

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

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)

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

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

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