Write the corresponding rectangular equation for the following parametric equation by eliminating t. Draw a graph of the plane curve using the rectangular equation. Indicate the direction of the curve obtained corresponding to increasing values of t using arrows.

x = 3t, y = 7t; −∞ < t < ∞

Transform the given rectangular equation into a polar equation.

x = 12

Test the polar equation for symmetry and sketch its graph:

r = (7/2) sin 3θ

Given the rectangular equation $x^2+y^2=121$, convert it to a polar equation that expresses $r$ in terms of $\theta$.

Transform the given rectangular equation into a polar equation.

$y^2=117x$

Graph the given polar equation.

$r=6\sin 3\theta$

Graph the polar equation $r=5+5\cos \theta$ and identify the type of graph it produces.