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
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.