# Math Help - Hypocycloid

1. ## Hypocycloid

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!

2. Okay, here's what I have so far:

The slope of the ladder would be rise over run, making the slope $-L/sqrt(1-L^2)$.
The derivative of the hypocyloid would start out to be:
$(2/3)x^(-1/3) x' + (2/3)y^(-1/3)y'= 0$
but how can I take the derivative of two things at once? I would need the speed in the x or speed in the y wouldn't I? To prove they these two things were tangent, I'd have to make the slopes equal, right?
Nevermind, got it!