Gallery of polar curves

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We see a collection of polar curves.

Lines

Horizontal lines

$\graph [polar]{a=1,r=a \csc (\theta )}$

Vertical lines

$\graph [polar]{a=1,r=a \sec (\theta )}$

Not through the origin

$\graph [polar]{b=1,m=1,r=\frac {b}{\sin (\theta )-m \cos (\theta )}}$

Circles

Centered on the x-axis

$\graph [polar]{a=1, r=a \cos (\theta )}$

Centered on the y-axis

$\graph [polar]{a=1,r=a \sin (\theta )}$

Centered at the origin

$\graph [polar]{a=1,r=a}$

Archimedean spiral

$\graph [polar]{r=\theta }$

Limaçons

With inner loop

$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{a=1,b=2,r=a+b \cos (\theta )}$ $\graph [xmin=-5,xmax=5,ymin=-.5,ymax=3.5,polar]{a=1,b=2,r=a+b \sin (\theta )}$

Cardioid

$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{a=1,b=a,r=a+b \cos (\theta )}$ $\graph [xmin=-5,xmax=5,ymin=-1,ymax=2.5,polar]{a=1,b=a,r=a+b \sin (\theta )}$

Dimpled

$\graph [polar]{a=3,b=2,r=a+b \cos (\theta )}$ $\graph [xmin=-10,xmax=10,ymin=-2,ymax=6,polar]{a=3,b=2,r=a+b \sin (\theta )}$

Convex

$\graph [xmin=-20,xmax=20,ymin=-7.5,ymax=7.5,polar]{a=5,b=2,r=a+b \cos (\theta )}$ $\graph [xmin=-20,xmax=20,ymin=-5.5,ymax=10,polar]{a=5,b=2,r=a+b \sin (\theta )}$

Rose curves

$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\cos (2\theta )}$

$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\sin (2\theta )}$

$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\cos (3\theta )}$

$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\sin (3\theta )}$