Plane intersection

AronH

Hi!
I have made this problem but I am not sure of it is visualization and final result.
"Find an equation of the straight line tangent to the curve of intersection of the surfaces x^3+3xi^2y^2+y^3+4xy-z^2=0 and x^2+y^2+z^2=11 at the point (1,1,3)."
I tried to put the two equations to be true and found a third equation then I calculated the gradient of it and found (11,10,-12) at the point (1,1,3).
Can anyone help me?
Thanks,


Aron