Question

Show that the graphs of r = aθ and rθ = a have an unlimited number of intersection points.

Answer 1

I know that the equation
\[r=a\theta\]
has the same graph as
\[-r=a(\theta+\pi)\]
and that the equation
\[r\theta=a\]
has the same graph as
\[-r(\theta+\pi)=a\]