1. The problem statement, all variables and given/known data Find the equations of both the tangent lines to the ellipse x2 + 9y2 = 81 that pass through the point (27, 3). One is horizontal the other is not. 2. Relevant equations 3. The attempt at a solution horizontal, easy: y = 3 x^2+9y^2=81 derivative: 2x + 18yy` = 0 y`= -x/9y at the point (27,3) the slope will be -1. y-3 = -(x-27) y= -x + 30 this solution is wrong according to my online assignment program, but I can't for the life of me see why.