Let T and N be the tangent and normal lines to the ellipse x2/9 + y2/4 =

Question:

Let T and N be the tangent and normal lines to the ellipse x2/9 + y2/4 = 1 at any point P on the ellipse in the first quadrant. Let xT and yT be the x- and y-intercepts of T and xN and yN be the intercepts of N. As P moves along the ellipse in the first quadrant (but not on the axes), what values can xT, yT, xN, and 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.