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1. Suppose that a surface \( S \) is defined by \[ z=f(x, y)=x^{2}+x y+y^{2}-2 x+2 y . \] a. Find ...
1. Suppose that a surface \( S \) is defined by \[ z=f(x, y)=x^{2}+x y+y^{2}-2 x+2 y . \] a. Find the equation of the tangent line to the curve \( z=f(x, 1) \). b. Find the equation of the tangent plane to \( S \) when \( x=1 \) and \( y=1 \).