Circle Equations and Properties

The video tutorial explains how to graph a circle from a given equation by converting it into standard form. It involves completing the square for both x and y parts of the equation, factoring the resulting trinomials, and identifying the circle's center and radius. The tutorial concludes with instructions on plotting the circle on a graph using the identified center and radius.

What is the standard form of a circle's equation?

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 + 2hx + 2ky = r^2

What is the first step in completing the square for the x part of the equation?

• Add the square of half the coefficient of x to both sides

• Subtract the constant term from both sides

• Multiply the equation by 2

• Divide the equation by the coefficient of x

When completing the square, what do you add to both sides for the y part if the coefficient of y is 4?

• 16

• 2

• 4

• 8

What are the factors of the x part of the equation after completing the square?

• (x + 2)(x + 2)

• (x - 2)(x - 2)

• (x + 1)(x + 1)

• (x - 1)(x - 1)

What is the center of the circle given by the equation (x - 1)^2 + (y + 2)^2 = 1?

• (-1, 2)

• (1, -2)

• (-1, -2)

• (1, 2)

How do you determine the radius from the equation (x - 1)^2 + (y + 2)^2 = 1?

• The square root of the right side

• Double the right side

• The right side itself

• The square of the right side

What is the radius of the circle with the equation (x - 1)^2 + (y + 2)^2 = 1?

• 2 units

• 1 unit

• 4 units

• 0.5 units

When graphing the circle, how many units do you move from the center to plot the circle?

• 3 units in each direction

• 1 unit in each direction

• 0.5 units in each direction

• 2 units in each direction

What is the significance of the point (1, -2) in the graph of the circle?

• It is the diameter of the circle

• It is the center of the circle

• It is a point on the circle

• It is the radius of the circle

Which direction do you move from the center to plot the circle?

• Up, down, left, and right

• Diagonally

• Only up and down

• Only right and left