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Curves Family Envelope, Math, Marketing Management
A curve which touches each member of a family of curves and which is touched at each point by some member of the family is called the envelope of the family of curves.
Example: Consider the family of straight lines
y = mx + a/m ,
where m is the parameter and a is some given constant.
We know that each member of the family touches the parabola y2 = 4ax. Also the parabola y2 = 4ax has at every point the tangent which is of the form y = mx + a/m . Hence y2 = 4ax is the envelope of the given family of lines.
Posted Date: 1/31/2012 10:54:30 PM | Location : United States
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