  We consider a problem similar to the well-known ladder box problem, but where
the box is replaced by an ellipse. A ladder of a given length, $s$, with ends
on the positive x and y axes, is known to touch an ellipse that lies in the
first quadrant and is tangent to the positive x and y axes. We then want to
find the height of the top of the ladder above the floor. We show that there is
a value, $s = s_0$, such that there is only one possible position of the
ladder, while if $s > s_0$, then there are two different possible positions of
the ladder. Our solution involves solving an equation which is equivalent to
solving a 4th degree polynomial equation.
