Eliminating the Parameter Final

Eliminate the parameter. Convert the parametric equation to rectangular.

x = 2 + 4t and y = -1 + 6t

• y = (3/2)x -4

• t = (x-2)/4

• y = x - 4

• y = (2/3)x + 4

The coordinates of a car at time t are given by x = 8 - t and y = 2t - 16. As t increases, which direction and path is the car traveling?

• left and up along the path y = 2x - 16.

• left and down along the path y = 2x.

• left and up along the path y = -2x.

• left and down along the path y = -2x.

The position of a particle at time t is given by x = 3 cos(t) and y = 3 sin(t), t: [0, 2π]. Which of the following describes the path of the particle?

• a circle of radius 3 centered at the origin starting right going counter-clockwise

• a circle of radius 3 centered at the origin starting down going clockwise

• a circle of radius 3 centered at the origin starting right going clockwise

• a circle of radius 3 centered at the origin starting up going counter-clockwise

The position of the blade of a fan at time t is given by x = cos(-t) and y = sin(-t). As t increases, which direction and path is the blade traveling?

• counter-clockwise around a circle centered at the origin of diameter 1.

• counter-clockwise around a circle centered at the origin of radius 1.

• clockwise around a cicle centered at the origin of diameter 1.

• clockwise around a circle centered at the origin of radius 1.

What curve do the parametric equations make? What is the direction of motion?

x=1+3cost

y=-2+3sint

• Circle. Counterclockwise, center at (-1, 2).

• Circle. Clockwise, center at (1, -2)

• Circle. Counterclockwise center at (1, -2)

• Circle. Clockwise, center at (-1, 2)

Which half of the curve will be graphed for the parametric equation:

x = 1 + 3cost

y = -2 - 4sint

π ≤ t ≤ 2π

• Right half

• Left half

• Top half

• Bottom half

Eliminate the parameter:
x = 8 + 2cos(t)
y = -6 + sin(t) 

• (x + 8)²/4 + (y + 6)² = 1
• (x - 8)²/4 + (y - 6)² = 1
• (x - 8)²/4 + (y + 6)² = 1
• (x - 8)²/2 + (y + 6)² = 1

Find a rectangular equation for the parametric function

x = -2 + 2t, y = 2 - t; for t = (-2, 2).

• y = -x +1 , -6<x<2

• y = -x + 1, -6<x<0

• y = -1/2x +1, -6<x<0

• y = -1/2x + 1, -6<x<2

Eliminate the parameter for the above parametric equation.

• y = 2x² + 1 , 2<x<3

• y = 2x² + 1, 7<y<17

• y = 2x² - 1, 2<x<3

• y = 2x² - 1, 7<y<17

which value would you change so the ellipse starts on the left and moves clockwise?

x = 8 + 2cos(t)

y = -6 + sin(t)

• change 2 to -2 and make the sine negative

• change the 8 to -8 and the -6 to a 6

• change 2 to -2 and keep the sine positive

• It is already doing that, no changes