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WebPrecalculus. Precalculus questions and answers. - A circle is a special case of an ellipse where a = b. It then follows that c? = a- 62 = a? - a’= 0, so c =0). (Therefore, the foci are at the center of the circle, and this is simply labeled as the center and not the focus.) The standard form for the equation of a circle is a (x - h)? + (y- k ... WebJan 13, 2024 · Let #P# be a point at a distance #d# from the center of a circle of radius #r#.The curve traced out by #P# as the circle rolls along a straight line is called a … The cardioid is the special case in which the point generating the roulette lies on the rolling circle; the resulting curve has a cusp. Depending on the position of the point generating the curve, it may have inner and outer loops (giving the family its name), it may be heart -shaped, or it may be oval. See more In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a … See more The earliest formal research on limaçons is generally attributed to Étienne Pascal, father of Blaise Pascal. However, some insightful investigations regarding them had been … See more • Roulette • Centered trochoid • List of periodic functions See more • "Limacon of Pascal" at The MacTutor History of Mathematics archive • "Limaçon" at www.2dcurves.com • "Limaçon of Pascal" at MathCurve See more The equation (up to translation and rotation) of a limaçon in polar coordinates has the form $${\displaystyle r=b+a\cos \theta .}$$ This can be … See more • Jane Grossman and Michael Grossman. "Dimple or no dimple", The Two-Year College Mathematics Journal, January 1982, pages 52–55. • Howard Anton. Calculus, 2nd edition, page 708, John Wiley & Sons, 1984. See more song and dance man book