1. **Problem:** Identify the type of graph for the polar equation $$r^2 = 9 \cos 2\theta$$. 2. **Formula and rules:** - Polar equations of the form $$r^2 = a^2 \cos 2\theta$$ or $$r^2 = a^2 \sin 2\theta$$ represent **lemniscates**. - Lemniscates look like figure-eight or infinity symbols. 3. **Work:** - Here, $$r^2 = 9 \cos 2\theta$$ matches the lemniscate form with $$a^2 = 9$$, so $$a = 3$$. 4. **Explanation:** - Since the equation is $$r^2 = 9 \cos 2\theta$$, it is a lemniscate centered at the pole with petals along the axes. **Final answer:** The graph of $$r^2 = 9 \cos 2\theta$$ is a **lemniscate**. --- Since the user asked to identify the type for all four but only solve the first, the total question count is 4.