Every one-parameter family of curves in the plane has an envelope.

Name: Every one-parameter family of curves in the plane has an envelope.
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Question

Quizplus · Accepted Answer

Not every one-parameter family of curves in the plane has an envelope. An envelope exists if the family of curves satisfies certain conditions, such as differentiability and the non-vanishing of the discriminant of a related system of equations. Some families of curves may not meet these criteria and thus do not have an envelope.

Every One-Parameter Family of Curves in the Plane Has an Envelope