Given:
The graph of a polar function is given.
[tex]\begin{gathered} r(\theta)=a\cos k\theta \\ \text{Period of }\cos k\theta=\frac{2}{k}\pi \end{gathered}[/tex]
From the graph,
[tex]\begin{gathered} k=2 \\ \text{Period of }\cos 2\theta=\pi \end{gathered}[/tex]
The graph of the polar equation,
[tex]r^2=9\cos (2\theta)[/tex]
Answer: option C)
