Answer:
The graph of polar equation is symmetric about the x-axis.
Step-by-step explanation:
The given polar equation is
[tex]r=-5-5\cos \theta[/tex]
If [tex](r,\theta)[/tex] and [tex](r,-\theta)[/tex] lie on the graph then the graph of polar equation is symmetric about the x-axis.
Substitute [tex]\theta=-\theta[/tex] in the given equation.
[tex]r=-5-5\cos (-\theta)[/tex]
Cosine is an even function.
[tex]r=-5-5\cos \theta[/tex] [tex][\cos (-\theta)=\cos (\theta)][/tex]
Point [tex](r,-\theta)[/tex] lies on the graph, therefore the graph of polar equation is symmetric about the x-axis.
