Worksheet: Graphing Parametric Curves

In this worksheet, we will practice graphing parametric curves.

Q1:

Anthony wants to graph the parametric equations 𝑥 = 2 𝑡 2 and 𝑦 = 3 𝑡 2 , where 0 𝑡 2 .

He has started to complete a table of values.

𝑡 0 0.5 1 1.5 2
𝑥 −2 −1 𝑎 1 2
𝑦 3 2.75 𝑏 𝑐 −1

Find the values of 𝑎 , 𝑏 , and 𝑐 .

  • A 𝑎 = 0 , 𝑏 = 1 , 𝑐 = 0
  • B 𝑎 = 2 , 𝑏 = 2 , 𝑐 = 0 . 7 5
  • C 𝑎 = 0 , 𝑏 = 2 , 𝑐 = 1 . 2 5
  • D 𝑎 = 0 , 𝑏 = 2 , 𝑐 = 0 . 7 5

Use the table of values to determine which of the following graphs is correct.

  • A
  • B
  • C
  • D

Q2:

Karim wants to graph the parametric equations 𝑥 = 2 𝑡 c o s and 𝑦 = 𝑡 s i n , where 0 𝑡 𝜋 .

He has started to complete a table of values.

𝑡 0 𝜋 4 𝜋 2 3 𝜋 4 𝜋
𝑥 2 2 𝑎 2 2
𝑦 0 2 2 𝑏 𝑐 0

Work out the values of 𝑎 , 𝑏 , and 𝑐 .

  • A 𝑎 = 0 , 𝑏 = 1 , 𝑐 = 2 2
  • B 𝑎 = 2 , 𝑏 = 0 . 0 2 7 , 𝑐 = 0 . 0 4 1
  • C 𝑎 = 2 , 𝑏 = 1 , 𝑐 = 2 2
  • D 𝑎 = 0 , 𝑏 = 1 , 𝑐 = 2 2

When Karim plots the coordinates on a graph, he is not entirely sure about the shape of the curve. What is the one thing he could do to find out more about the shape of the curve?

  • AKarim could extend his table of values; for example, he could increase 𝑡 by increments of 𝜋 8 rather than 𝜋 4 .
  • BKarim could extend the value of 𝑡 to be lower than 0.
  • CKarim could extend the value of 𝑡 to be greater than 𝜋 .

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