This question seems impossible to me, because you know the lamp is at the intersection of the two tangent lines, but you are given no clue as to where the lower tangent line is. It does not intersect the ellipse at the x-axis, because if it did then it would be a perfectly vertical line.
You can figure out the location of the lamp by intersecting the tangent with x-intersect -5 with the line x=3. So you don't need to know anything more about that second tangent...
Originally Posted by Chokfull