The paraboloid LaTeX: z=6-x-x^2-2y^2z = 6 − x − x 2 − 2 y 2 intersects the plane LaTeX: x=1x = 1, resulting in a parabola. Similarly, the function LaTeX: zz is intersected by the plane LaTeX: y=2y = 2 , resulting in another parabola, perpendicular to the first one. Find the parametric equations for the tangent lines corresponding to each of these parabolas at the point LaTeX: \left(1,2,-4\right)( 1 , 2 , − 4 ).