Parametric Equations - Concept Check

What is the purpose of using a parameter in parametric equations?

• To control the values of x and y

• To plot the points on the coordinate plane

• To define the values of t

• To calculate the values of x and y

What type of plane curve is traced by the parametric equation x = 2 - 3t and y = 1 - 2t?

• Parabola

• Circle

• Line

• Ellipse

For the parametric equation x = 4cos(t) and y = 4sin(t), what shape does the plane curve represent?

• Ellipse

• Parabola

• Line

• Circle

What is the benefit of using a parametric equation to model the path of a projectile?

• Represents horizontal distance and height at any point in time

• Represents vertical distance and time

• Represents speed and acceleration

• Represents angle and velocity

In the parametric equation x = 2t - 1 and y = -t + 3, what is the point when t = 2?

• (9, -2)

• (4, 0)

• (-5, 5)

• (3, 1)

For the parametric equation x = 4cos(t) and y = 4sin(t), what is the shape of the plane curve when t is in the interval from 0 to 2π?

• Circle

• Line

• Parabola

• Ellipse

What is the parametric equation for a line passing through the points (3, 4) and (7, 8)?

• x = 3 + 4t, y = 4 + 4t

• x = 3t, y = 4t

What type of plane curve is traced by the parametric equation x = 5cos(t) and y = 3sin(t)?

• Circle

• Line

• Parabola

• Ellipse

In parametric equations, the dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable. True or False?

• Cannot be determined

• False

• True

In parametric form, how can the equation y = x^2 be described?

• x = t and y = t

• x = t^2 and y = t^3

• x = t^2 and y = t

• x = t and y = t^2