Use the note in the preceding problem to prove that in the Ladder Problem, the moving ladd...

Use the note in the preceding problem to prove that in the Ladder Problem, the moving ladder is the envelope of the astroid x2/3 + y2/3 = a2/3, where a is the length of the ladder. (To get started, let the x- and y-intercepts of the line representing the ladder be t and respectively; the equation of the line is then