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Families of Polar Curves: Circles, Cardiods, Limaçon, Roses & Conic Sections

Videos, worksheets, solutions, and activities to help PreCalculus students learn how to recognize and graph families of polar curves: Circles, Cardiods, Limaçon, Roses & Conic Sections.

Families of Polar Curves: Circles, Cardiods, and Limaçon :
Recognizing certain special polar curves can help us graph them or derive their equations. Circles, cardioids and limacon are all from the same family of polar curves. Other families include roses and conic sections. Students should understand and memorize the equations for these families of polar curves and their special cases.
How to graph the special cases of the family r = a + b cos (theta) when a or b = 0.
Families of Polar Curves: Roses :
One family of polar curves that we will see frequently when dealing with graphing polar equations and polar symmetry is the polar rose. It is important to be able to recognize the general equation of a polar rose, and to use that equation to interpret the symmetry and number of petals. The general equation of a polar rose is similar to that of the family of circles and cardioids.

Families of Polar Curves: Conic Sections :
One can use polar coordinates to describe polar conic sections, or conic sections with one focus at the origin of the polar coordinate system. Polar conic sections are described by a family of polar equations, and can be graphed using methods of graphing polar equations. Polar conic sections use similar methods for graphing as the rose or the cardioid.
How to describe the polar equations of conic sections.

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