Parametric and Cartesian Parabola problem

Prove that the equation of the tangent to the parabola y^2=4ax at the point P (at^2,2at) is yt= x+at^2. If this tangent meets the axes at X and Y, prove that XY = atsqrt{1+t^2}

I'm horrendously stuck. Even working out the gradient of the tangent just throws so many a's and x's my way I can't sort it out. I appeal for help /sci/

Okay bitch. Solved your problem:

Gradient of tangent = t

x - at^2 = t(y - 2at)

x - at^2 = yt - 2at^2

x + at^2 = yt

Part 2:

0 + at^2 = yt

Y = at

x + at^2 = yt

X = -at^2

XY = sqrt { (at)^2 + (at^2)^2 }

   = sqrt { a^2t^2 + a^2t^4 }

   = sqrt { a^2t^2 (1 + t^2) }

   = at sqrt { 1 + t^2 }

BITCH NIGGA