Answer
Any value, except 0.
Work Step by Step
If two curves intercept at right angles, then the product of their slope must be $-1$, so we must derivate the functions and check that equation to see if there's any restriction for $a$. That is done on the image below.
The equation which relates the $x$ where the interception occurs with $a$: $a=\frac{x-1}{2}$ has no restriction, so $a$ could be any value. But the first function $y_{1}=\frac{a}{x-1}$ does not exist in $x=1$, since there cannot be 0 in the denominator.
If the interception occurs at $x=1$ (which is not allowed) we would have $a=0$. So this is the only forbidden value of $a$.
