'm stuck on this question about identifying the following loci:
<br />
\begin{array}{l}<br />
 a)\theta  = a \\ <br />
 b)\varphi  = a \\ <br />
 c)r = a \\ <br />
 d)r = \theta  = a \\ <br />
 e)r = \theta  = \varphi  \\ <br />
 \end{array}<br />

My thinking is as follows:
a) a vertical cylinder?
b)cone with vertex at origin?
c) sphere of radius a, centred at origin?
e) line through the origin?

Please explain what the loci are as I'm not very good at just visualising it.