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

Feb 20, 2016

There is no such curve.

#### Explanation:

At $\left(1 , 2\right)$, the denominator $\sqrt{y - x} - x$ is $0$.

So, $\frac{y}{\sqrt{y - x} - x}$ cannot be equal to a constant at $\left(1 , 2\right)$.

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 $\left(1 , 2\right)$