Question

A curve which touches each member
of a given family of curve
is called
of that family.​

Answer 1

Answer:

A curve which touches each member of a given family of curves is called envelope of that family.

Answer 2

A curve which touches each member of a given family of curve is called envelope of that family.

In three dimensions, in a plane each one of a family of curves is tangential. To each one of the family surface is tangent . At some point , to each member of the family is tangent .

Classically, a point on the envelope can be thought of as the intersection of two "infinitely adjacent" curves, i.e. the boundary of the intersection of adjacent curves. This idea can be generalized to higher dimensions, such as shells of surfaces in space.

To have an envelope, each member of a family of curves must be a differentiable curve. Otherwise, the concept of tangents does not apply and smooth transitions through members are required. But these conditions are not enough. Certain families may not have envelopes. 

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