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

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

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.