1) Pick a hyperbolic paraboloid and write down the corresponding function, f.

2) Pick a point A(a,b) in the xy-plane such that f(a,b) is not zero.

3) Find and write the parametric equation of a line passing through A on the xy-plane. The line has to be in the xy-plane, so, the third component of the parametric equation of the line is zero.

4) Project the line onto the surface given by the function f. Write the corresponding parametric equation.

5) Use the derivative of the projection, which gives the tangent vector to the curve and write down the corresponding derivative

6) By using the derivative and the tangent vector find and write the equation of the tangent line.