# Charpit PDE, rays parallel or perpendicular to boundary

The rays are all possible curves $$(x(\tau), y(\tau))$$. The derivation of the equations is clear and the condition of defining $$p_0, q_0$$ is $$\frac{dx_0}{ds}\frac{dy_0}{d\tau} - \frac{dy_0}{ds}\frac{dx_0}{d\tau} \neq 0$$. But:

1) Why is this condition equivalent to "rays not being parallel to $$\Gamma$$"?

2) What is a similar condition (and why does it hold) when we want the rays to be orthogonal to $$\Gamma$$?

Any help appreciated!