Prove slopes of two curves are equal

Question

Let $f(x,y,c) = 0$ and $f(x,y,k) =0$ define two integral curves of homogenous first order differential equation . if $p_1$ and $p_2$ are respectively the points of intersection of these curves with an arbitrary line $y = mx$ . Then we have to prove that the slopes of these two curves at $p_1$ and $p_2$ are equal .

I thought about it a lot. But not got any start how to do it .

Please can anyone tell me how to start it.

Answer 1

Homogeneous means in this case $y'=g(y/x)$?

Then on the line $y=mx$ all intersecting solutions have slope $y'=g(m)$.