Math 124, Sections E and G: bonus problem

(Due November 26)

Here is the equation of an ellipse: x2/9 + y2/25 = 1. Consider a point P lying on the ellipse in the first quadrant. Let LN be the ``normal line'' through P. That is, LN is the line through P which is perpendicular to the tangent line at P. Let xN be the x-intercept of the normal line, and let yN be its y-intercept. As P goes from (3,0) to (0,5), how do xN and yN behave?

First make a guess as to their behavior, just based on the picture and your intuition. Then use calculus to solve the problem. [It's probably easiest to use implicit differentiation.]

As with the first extra-credit problem, you may hand in joint work, collaborating in groups of at most four. In addition to your names, please include the section for each collaborator.

(This same problem is available in PDF format here.)

I've written a solution to this problem (PDF format).

Questions or comments? E-mail me at palmieri@math.washington.edu.

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Last modified: Mon Apr 29 12:13:41 PDT 2002