Consider the ellipse (x - 3)² + ((y - 4)²/4) = 1. Find the two tangent lines of it through the origin by the following steps:
i.) For any point (a, b) on the ellipse, write down a normal vector of the ellipse at this point.
ii.) For the same point (a, b) as in (i), write down the equation of the tangent line at this point.
iii.) Since (a, b) is on the ellipse and (0, 0) is on the tangent line at this point, one now has a system of equations for the unknowns a and b. Solve for a and b to get the tangent lines.
