Conic sections (the circle, ellipse, parabola and hyperbola) can all be represented by an equation in polar coordinates:
where is the semilatus rectum and is the eccentricity of the curve. For the circle, ellipse, parabola and hyperbola, the eccentricity has the values , , and , respectively.
One focus of such a conic is at the origin. After selecting values of and , you can use the "polar angle" slider to trace out the polar curve by sweeping from 0 to . For , the plot generates both branches of a hyperbola.