find the equations of the lines that are tangent to the eclipse x^2 + 4y^2 =16 and that also pass through the point (4,6)

i implicitly differentiated it and i got -x/4y

then i plugged the point (4,6) to find the slope and got an equation that is 6y + x -40 = 0 but according to the text the answers are x-4=0 and 2x-3y + 10 = 0

what did *I do wrong and how do i solve this problemusing implicit differentiation.

edit: typo