MATH225 Lecture Notes - Lecture 2: Evolute, Hyperbola, Hyperbolic Function
7 Apr 2016
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Document Summary
A curve which touches each member of a given family of curves is called envelope of that family. Procedure to find envelope for the given family of curves: Case 1: envelope of one parameter family of curves. Let us consider y = f(x, ) to be the given family of curves with " as the parameter. Step 1: differentiate w. r. t to the parameter partially, and find the value of the parameter. Step 2: by substituting the value of parameter in the given family of curves, we get the required envelope. Special case: if the given equation of curve is quadratic in terms of parameter,i. e. a 2+b +c=0, then envelope is given by discriminant = 0 i. e. Special case: if the given equation of curve is quadratic in terms of parameter,i. e. a 2+b +c=0, then envelope is given by discriminant = 0 i. e. b2- 4ac=0. Case 2: envelope of two parameter family of curves.
