畫圖問題 (外國試題, 幫幫手唔該)

1, Sketch the locus r = e^(ax) and identify the types of the graph.

Please see http://web.hku.hk/~linchak/e%5E(ax).jpg
the left curve is when a>0,
the right curve is when a<0
when a=0, the curve in fact is a unit circle

About the types of the graph, I am not too sure,
but I suggest it is one type of spiral

For this kind of Questions, you should first assume a= sth, (e.g. -0.5,1, 2, etc)
then You can plot it with some graphical calculator or some programme such as winplot, mathematica, etc...
OR if you don't have any tools
you can simply draw a table to test the point and draw it.
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2, Discuss the Spiral of Archimedes and find the general formula of the locus.

For this questions, I usggest you can refer to http://www-groups.dcs.st-and.ac.uk/~history/Curves/Spiral.html
and
http://www-groups.dcs.st-and.ac.uk/~history/Java/Spiral.html
(given your computer support java)

genearl formula: r = a*theta