Edexcel a level maths range help

Can you see it now ?

Can you see on the graph where the line x=k must be if it intersects the graph at two points?

Oh I think I got it now. I think we have to put dx/dy=0 which means that x(1 2y)=0. If we put 1 2y=0, we will get y= -1/2, and if we substitute this back into x=ye^2y we will get -1/2e^-1. This means that k must be greater than -1/2e^-1 but less than 0, which will give us -1/2e^-1<k<0. Does that sound right?

Yes that's correct.