PS4 Q6 can be simplified considerably

[ruds]

Namely, in 6b, you just need to encode that each (x, y) in our target function satisfies the equation written in 6a for (x_0, y_0):

L^2 = (x-\frac{y}{y'})^2 + (y-\frac{x}y')^2

That means that 6c can be reduced to 3 or so lines (a few more if you want to be more deliberate about simplifications), ending in (I believe)

(y(y')^{-3} + x) (xy'-y)y''

In any case, you can use implicit differentiation of the hypocycloid equation, solve for y', and show that the first factor zeros out.