Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ

Answer 1

It is symmetric about the x-axis

Answer 2

Answer:

The graph of polar equation is symmetric about the x-axis.

Step-by-step explanation:

The given polar equation is

$r=-5-5\cos \theta$

If $(r,\theta)$ and $(r,-\theta)$ lie on the graph then the graph of polar equation is symmetric about the x-axis.

Substitute $\theta=-\theta$ in the given equation.

$r=-5-5\cos (-\theta)$

Cosine is an even function.

$r=-5-5\cos \theta$                   $[\cos (-\theta)=\cos (\theta)]$

Point $(r,-\theta)$ lies on the graph, therefore the graph of polar equation is symmetric about the x-axis.