How do you find the envelope of a family of curves?

Dicembre 21st, 2020 | by Marcello Colozzo |

How do you find the envelope of a family of curves?
Fig. 1


Exercise

Determine the envelope of the family of plane curves:


Solution
The system of equations that interests us is


where


for which


From the second:


so (0,0) is a basis point. Discarding this solution, we proceed:


hence the Cartesian representation of the envelope drawn in fig. 1.

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