Equation of Envelope of Family of Curves/Examples

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Examples of Equation of Envelope of Family of Curves

Example: $y = 2 m x + m^2$

Consider the family of curves $\FF$ embedded in the Cartesian plane defined by the equation $E$:

$E: \quad y = 2 m x + m^2$

where $m$ is the parameter of $\FF$.


The envelope of $\FF$ is the parabola whose equation is:

$y = -x^2$