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Please help me. I included my answers. Please check to make sure that my way is right.

1. IF f(x,y) = x^2 +4y^2, find the gradient vector f(2,1) and use it to find the tanenet line to the level curve f(x,y) = 8 in the xy-plane at the point (2,1).

I solved this way:

f(x,y) = x^2 + 4y^2

gradient f(x,y) = <fsubx, fsuby>

fsubx = 2x

fsuby = 8y

therefore, gradient f(x,y) = <2x,8y>

gradient f(2,1) = <4,8>

f(x,y) = 8

HOW DO I FIND THE EQUATION OF TANGENT LINE?????

- I know how to find the equation of tangent plane, but i dont know how to find line. If you can tell me how to find it, i would greatly appreciate your help and intellect.

AND, please make sure that What i did until now is right.

Thank you so much.