Is the contract curve orthogonal to the priceline?
You write that the slope of one line is px/py and of another is -px/py. Take a piece of paper and draw the line y=2x and y=-2x are they orthogonal (answer: no)? In particular case the lines y=x and y=-x are orthogonal.

If we regard it more formally, the vectors are orthogonal if the product is 0. Thus, 

&lt;1,-p&gt;*&lt;1,p&gt; = 1-p^2 


This is 0 only if p=1 or p=-1, i.e. if the quantities of the 1-st and 2-nd good are equal.

To take a loon on it. Consider the wealth distribution something like 1-st player: [5;
15], 2-nd: [25;5], thus ex=30,ey=20,px/py = 2/3, then it looks like this: 

p.s. Calculations and plotting were made with pyEdgeworthBox package (I wrote it).