Parametric Equations in Algebraic Contexts
Math ⇒ Algebra
Parametric Equations in Algebraic Contexts starts at 11 and continues till grade 12.
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Describe how to graph the parametric equations x = t^2, y = t + 1 for t in [-2, 2].
Describe the process of converting the parametric equations x = 2t + 1, y = 3t - 4 into a Cartesian equation.
Explain why parametric equations are useful in describing the motion of objects.
Given the parametric equations x = 2t + 1 and y = 3t - 4, eliminate the parameter t to find the Cartesian equation relating x and y.
Which of the following is a correct set of parametric equations for the line y = 2x + 3?
(1) x = t, y = 2t + 3
(2) x = 2t + 3, y = t
(3) x = t, y = t^2 + 3
(4) x = t^2, y = 2t + 3
Which of the following is a parametric representation of the parabola y = x^2?
(1) x = t, y = t^2
(2) x = t^2, y = t
(3) x = t, y = 2t
(4) x = t^2, y = t^3
Which of the following is NOT a possible advantage of using parametric equations?
(1) Describing curves that cannot be represented as functions
(2) Representing motion along a path
(3) Simplifying the process of finding intersections
(4) Describing only straight lines
Which of the following parametric equations represents a straight line?
(1) x = t, y = t^2
(2) x = 2t + 3, y = 5t - 1
(3) x = cos t, y = sin t
(4) x = t^2, y = t^3
Fill in the blank: The parameter in parametric equations is often denoted by the letter _______.
Fill in the blank: The parametric equations x = a cos t, y = a sin t, for t in [0, 2π], represent a circle of radius a centered at the _______.
Fill in the blank: The parametric equations x = a cosθ, y = b sinθ represent a(n) _______.
Fill in the blank: The parametric equations x = r cosθ, y = r sinθ represent a circle of radius _______.
True or False: Every Cartesian equation can be written in parametric form.
True or False: The parametric equations x = cos t, y = sin t, for t in [0, 2π], trace out a full circle.
True or False: The parametric equations x = t, y = t^2 represent a parabola opening upwards.
True or False: The parametric equations x = t^2, y = t^3 + t^2 can be used to describe a curve that passes through the origin.
