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An Archimedean spiral, increasing distance from the pole as $\theta$ increases.

A limaçon without a loop because the coefficient of $\cos(\theta)$ is not less than the constant term.

A logarithmic spiral, which continuously winds around the pole and moves away from it.

A cardioid if $a > 0$, with the cusp at the pole and greatest distance $2a$ from the pole.

A circle with a radius $a$ if $a > 0$, centered to the left/right of the pole on the horizontal axis.

A cardioid (if $a > 0$) with the cusp away from the pole on the horizontal axis.

A cardioid or circular shapes depending on $\theta$ range.

A shifted circle or cardioid depending on the value of $a$.

A limaçon with a loop, since the coefficient of $\sin(\theta)$ is less than the constant term.

A rose curve with $2n$ petals, because $n$ (here $n=2$) is even, so the curve has 4 petals.

A rose curve with $2n$ petals when $n$ is even (in this case, with 4 petals).

A limaçon which may or may not have an inner loop.

A limaçon with an inner loop if $-1 < a \leq 1$ and a cardioid if $a = 1$.

An inverse logarithmic spiral winding towards the pole.