CIE A Level Maths: Pure 3复习笔记4.3.3 Parametric Equations - Sketching Graphs

Parametric Equations - Sketching Graphs

How do I sketch a graph from parametric equations? 

  • Plotting a graph is covered in Parametric Equations - Basics


  • Still find the key features of a graph …
    • … the y-axis intercept
    • … the x-axis intercept(s)
    • … asymptotes
    • … location of (and if required coordinates of) stationary points (see Parametric Differentiation)
  • Sketch these points and join up accordingly



Exam Tip

  • Not all curves defined parametrically lead to familiar shaped graphs and it may be worth plotting a few extra points by calculating them.
  • Your calculator may be able to produce a table of values quickly, however, remember you are sketching and not plotting.
  • It may be easier to find the Cartesian equation first and draw the graph from that – this will depend on the question.
  • It is only a definite strategy if you cannot make progress otherwise.
  • If you are given the sketch of a graph it is usually only for reference and can be used to check answers for axes intercepts, etc.

Worked Example