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:
- $y = -x^2$