Lesson: Conversion between Parametric and Rectangular Equations

In this lesson, we will learn how to convert from the parametric form of an equation to its equivalent rectangular form and vice versa.

Video

12:31

Sample Question Videos

  • 02:06
  • 01:55

Worksheet: 14 Questions • 2 Videos

Q1:

Use the fact that coshsinh𝑥−𝑥=1 to find a parametrization of the part of the hyperbola 𝑥25−𝑦81=1 that contains the point (−5,0).

Q2:

The first figure shows the graphs of cos2𝜋𝑡 and sin2𝜋𝑡, which parameterize the unit circle for 0≤𝑡≤1. What do the two functions graphed in the second figure parameterize?

Q3:

What is the length of 𝐴𝐵?

Find a parameterization of the segment 𝐴𝐵 over 0≤𝑡≤1.

Find 𝑓 and 𝑔 so that 𝑥=𝑓(𝑡), 𝑦=𝑔(𝑡) parameterizes 𝐴𝐵 over 0≤𝑡≤5.

Using the functions above for 0≤𝑠≤5, what is the distance between the point (1,1) and the point (𝑓(𝑠),𝑔(𝑠))?

The parameterization of 𝐴𝐵 above is an example of an {arc-length parameterization} of a plane curve. Find an arc-length parameterization 𝑥=𝑓(𝑡), 𝑦=𝑔(𝑡) of 𝐴𝐶, where 𝐶=(13,6) and the parameter starts at 𝑡=0. Give the interval used.
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