AP Pre-Calculus: Parametric Equations for Lines and Circles

What is the slope-intercept form of a line equation?

• y = mx + b

• y = b + mx

• x = my + b

• x = b + my

In parametric equations, what do you need besides a point to define a line?

• A second point

• The slope

• The rate of change for x and y

• The y-intercept

How do you calculate the rate of change for x in parametric equations?

• Add the y-values and multiply by the change in t

• Subtract the x-values and divide by the change in t

• Subtract the y-values and divide by the change in t

• Add the x-values and multiply by the change in t

What is the parametric equation for x(t) if the line passes through (-1, 3) and (3, 6)?

• x(t) = -1 + 4t

• x(t) = 3 + 4t

• x(t) = -1 + 3t

• x(t) = 3 + 3t

Which of the following is a method to verify parametric equations for a line?

• Finding the midpoint

• Calculating the area under the curve

• Graphing the equations

• Using the quadratic formula

What is the standard equation of a circle centered at the origin?

• x^2 - y^2 = 2r

• x^2 + y^2 = 2r

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

How do you modify the circle equation if the center is at (h, k)?

• (x - h)^2 + (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

What is the parametric equation for x(t) of a circle with radius 2 centered at (2, -4)?

• x(t) = 2 + 2cos(t)

• x(t) = 2 + 2sin(t)

• x(t) = 2cos(t) + 4

• x(t) = 2sin(t) + 4

What is the parametric equation for y(t) of a circle with radius 2 centered at (2, -4)?

• y(t) = -4 + 2cos(t)

• y(t) = -4 + 2sin(t)

• y(t) = 2 + 2cos(t)

• y(t) = 2 + 2sin(t)

What is the radius of a circle if the equation is (x - 2)^2 + (y + 4)^2 = 4?

• 1

• 2

• 3

• 4