Polar Graphing Calculator

This tool draws a polar curve and then says what it is. Choose one of seven standard forms, from a rose or a limacon to a lemniscate, a spiral or a conic section, set the constants and the range of theta in degrees, and it returns the plot on a polar grid, a table of theta against r and the matching x and y, the largest and smallest radius with the angles they occur at, the petal count or shape class, which of the three standard symmetry tests the equation passes, and the area the radius sweeps. It is a menu of named forms rather than a free equation box, because a parser that half understands what you typed is worse than a list that is honest about its range.