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Curves Family Envelope, Math, Marketing Management

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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.

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