with f(x,y) find equation of tangent line and projection parallel to x and y axises

[njcountrygirl]

Hello, any help would be must appreciated. I have two questions that I have been working on:

first, let f(x,y)=x³y²

1. find the equation of the tangent line to the above surface at the point (2,1,8) whose projection onto the XY plane is parallel to the x axis

2. find the equation of the tangent line to the above surface at the point (2,1,8) whose projection onto the XY plane is parallel to the y axis

I know that first I need to find:

F_x=3x²y²
then F_x(2,1,8)=12
and F_y=2x³y
then F_y(2,1,8)=16

I am not sure where to go from there to find the two tangent lines. I think that for the line parallel to the x axis I need to find the tangent vector first then just translate it into an equation, which I am also not positive on how to do.

Like I mentioned in the beginning, any help would be greatly appreciated!