Hello, I have to prove that a unit length ladder is tangent to the hypocycloid x^(2/3) + y^(2/3) = 1 at all times in the first quadrant as it falls to the ground. The simple image of the rotating circle creating the hypocycloid confirms this. I'm having a little trouble proving this, however, as it seems obvious that the slopes should just equal each other, however I'm having trouble determining a formula for the ladder. Can I use a^2 + b^2 = 1 or is there an easier way/better forumla? Thanks for all help!