We started learning about conic sections last week, and our assignment asks us to prove that, for the parabola

y^2=4px

the tangent line at point P(x1, y1) can be written as so:

y1*y=2p(x+x1)

I'm a little confused about how to proceed. I have that the slope will be

dx/dy = y/2p

but am unsure where to go from here.

Thanks!