Chapter 2.P, Problem 15P

Let T and N be the tangent and normal lines to the ellipse $x^2/9+y^2/4=1$ at any point P on the ellipse in the first quadrant. Let $x_T$ and $y_T$ be the x- and y-intercepts of T and $x_N$ and $y_N$ be the intercepts of N. As P moves along the ellipse in the first quadrant (but not on the axes), what values can $x_T,y_T,x_{N,}$ and $y_N$ take on? First try to guess the answers just by looking at the figure. Then use calculus to solve the problem and see how good your intuition is.