Point p is moving on a curve given by:

x=bt^2, y=2bt

now the Cartesian equation i worked out to be is:

y=2b(x/b)^0.5 (as you make t the subject of x)

The part i am stuck on is finding the equation of the normal at P (bt^2,2bt), which is x+y=at^3+2at i think but not to sure how to show, if Q was the intersection of the normal with the x axis i let y=0 and i know how to do that, how to calculate the velocity at Q when t=7 seconds?

i have figured out this as well:

dx/dt= 2bt, dy/dx= 2b so dy/dx=1/t?

thanks giovanni