Parametric Equations Worksheet
Explore parametric equations, their graphs, and conversions to rectangular form with this Grade 9 math worksheet.
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Parametric Equations Exploration
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Consider the parametric equations: x = t + 1 and y = t^2. Complete the table below for the given values of t.
t
x = t + 1
y = t^2
-2
-1
0
1
2
2. Using the table from Question 1, plot the points (x, y) on the coordinate plane below. Connect the points to sketch the curve.
3. Eliminate the parameter 't' from the following parametric equations to write them in rectangular form (an equation involving only x and y).
a) x = t + 3, y = 2t - 1
y =
b) x = 3t, y = t^2
y =
4. Which of the following pairs of parametric equations represents a circle?
x = t, y = t^2
x = cos(t), y = sin(t)
x = t + 5, y = t - 2
x = t^2, y = t^3
5. A projectile's motion is described by the parametric equations: x(t) = 20t and y(t) = 2 + 15t - 4.9t^2, where x is the horizontal distance in meters, y is the vertical height in meters, and t is time in seconds. What is the initial height of the projectile?
6. Parametric equations always represent a straight line.
True
False