Polar Circles and Symmetry Tests Worksheet with Answer Key

What's on the worksheet

1. Without converting to rectangular form, give the center (as a rectangular point) and the radius of each circle.
   r = -7r = 10\cos\thetar = -12\sin\thetar = \dfrac{5}{2}\sin\thetar = 3\sqrt{2}\cos\theta
2. The figure shows three circles, C_1, C_2 and C_3, on a polar grid whose rings are 1 unit apart.
3. A circle is symmetric about a line exactly when the line passes through its center, and symmetric about a point exactly when that point is its center.
   r = 2\sqrt{3}\cos\thetar = -5
4. The graph of r = aθ passes through the rectangular point (−4, −2).
5. The point (r, θ) moves on the circle r = -10θ as θ increases.