# Sketching a Phase portrait / dynamical system - finding the limit?

I have the question to sketch a phase portrait of the following, $$\dot{x} = 3y^2 - 25x^2$$ $$\dot{y} = 50xy$$

I have solved this to get $$y(y^2 - 25x^2) = C$$ To sketch the phase portrait I let C = 0 and so have a saddle point around (0,0) with the lines $$x=0$$, $$y=5x$$ and $$y=-5x$$.

I think this is okay, but then I am asked the following, in the case where $$x(0) = -1$$ and $$y(0) = -6$$ what is the value of $$\frac{x(t)}{y(t)}$$ in the limit as $$t \rightarrow \infty$$?

I have tried substituting in these values to my solution to get the constant = -66 but I am not sure where to go from there.

Thanks for any help.