Question

What is the slope of the tangent line of `y/(sqrt(y-x)-x) =C`, where C is an arbitrary constant, at `(1,2)`?

Answer 1

There is no such curve.

Explanation:

At `(1,2)`, the denominator `sqrt(y-x)-x` is `0`.

So, `y/(sqrt(y-x)-x)` cannot be equal to a constant at `(1,2)`.

Here are three graphs in the family.
Red has `C=1`
Blue has `C=4`
Black has `C=40`

As you can see, as `C` increases the curve gets closer to the point `(1,2)`