Consider the first quadrant in the $OXY$ plane in $\mathbb{R}^2$. Point $O$ is the origin and the points $P$ and $Q$ are chosen on the $y$-axis and the $x$-axis, respectively as it is showed in the figure below. We create a family of line segments like $PQ$ in a way that $OP+OQ=10$.
$1.$ Determine the equation of the curve which appears by drawing more and more such line segments.
$2.$ Suppose we want to investigate a similar problem in the three dimensional case. Consider the first octant of the $OXYZ$ in $\mathbb{R}^3$. Then we create a family of plane segments such that $OP+OQ+OR=10$. Then what would be the equation of the surface which will arise by drawing infinitely many such planes.
This link in wikipedia explains anything you want about finding envelopes. God bless wiki! :)
The solution to this problem is a piece of parabola. The procedure is thoroughly explained in the link I mentioned.