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Lesson: Graphing Parametric Curves

Worksheet • 2 Questions

Q1:

Karim wants to graph the parametric equations π‘₯ = 2 𝑑 c o s and 𝑦 = βˆ’ 𝑑 s i n , where 0 ≀ 𝑑 ≀ πœ‹ .

He has started to complete a table of values.

𝑑 0 πœ‹ 4 πœ‹ 2 3 πœ‹ 4 πœ‹
π‘₯ 2 √ 2 π‘Ž βˆ’ √ 2 βˆ’ 2
𝑦 0 βˆ’ √ 2 2 𝑏 𝑐 0

Work out the values of π‘Ž , 𝑏 , and 𝑐 .

  • A π‘Ž = 0 , 𝑏 = βˆ’ 1 , 𝑐 = βˆ’ √ 2 2
  • B π‘Ž = 2 , 𝑏 = βˆ’ 0 . 0 2 7 , 𝑐 = βˆ’ 0 . 0 4 1
  • C π‘Ž = 2 , 𝑏 = βˆ’ 1 , 𝑐 = βˆ’ √ 2 2
  • D π‘Ž = 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 the value of 𝑑 to be greater than πœ‹ .
  • BKarim could extend his table of values; for example, he could increase 𝑑 by increments of πœ‹ 8 rather than πœ‹ 4 .
  • CKarim could extend the value of 𝑑 to be lower than 0.

Q2:

Anthony wants to graph the parametric equations π‘₯ = 2 𝑑 βˆ’ 2 and 𝑦 = 3 βˆ’ 𝑑 2 , where 0 ≀ 𝑑 ≀ 2 .

He has started to complete a table of values.

𝑑 0 0.5 1 1.5 2
π‘₯ βˆ’2 βˆ’1 π‘Ž 1 2
𝑦 3 2.75 𝑏 𝑐 βˆ’1

Find the values of π‘Ž , 𝑏 , and 𝑐 .

  • A π‘Ž = 0 , 𝑏 = 2 , 𝑐 = 0 . 7 5
  • B π‘Ž = 2 , 𝑏 = 2 , 𝑐 = 0 . 7 5
  • C π‘Ž = 0 , 𝑏 = 2 , 𝑐 = 1 . 2 5
  • D π‘Ž = 0 , 𝑏 = 1 , 𝑐 = 0

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

  • A
  • B
  • C
  • D
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