Is there an intersection at the origin of the graph: $r=2+3cos\theta$

Question

Question

Is there an intersection at the origin of the graph: $r=2+3cos\theta$

I have realized that if I was to graph the equation into a graphing calculator and zoom at the pole, there were no intersection at the point but then I thought this was strange so I did some calculations

I know that if r=0 then that is an intersection at the pole so I set it to 0 and realize that it is possible to get a value $\theta$ which satisfies r being zero,

Why does the calculator show otherwise?

Answer 1

If we plot the graph:

We see there is in fact an intersection at $r=0$. The graphing calculator you used probably did a cartesian plot.