Homework due Monday, February 3rd

5. (2 points) On your constructed parabola, pick a point on the parabola and measure the distance from the point to the focus and the distance from the point to the directrix (pick the shortest possible distance). Repeat this process and record the measurements. Make some conjecture about the relationship between these two distances.

6. (2 points) Construct a hyperbola using envelopes by repeating the same instructions for the ellipse except that the focus is placed outside the circle, not inside.
7. (2 points) Another way of constructing a parabola is to draw two non-parallel line segments of the same length (say 6 inches). Mark off every half inch, and number them. (If you use a 6 inch line segment, you would use the numbers 1 through 12.) Be sure to number the marks in opposite order on the second line segment. When you draw line segments between corresponding numbers, you will create the envelope of a parabola. Show an example on paper. (You can find an animated example if you click on Figure 1 at this site.)

8. (2 points) Look at Clifford Singer's Smarandacheian Composition at his web site and identify as many conic sections as possible. (1 bonus point if you can name who the composition is named for with an additional bonus point if you can describe his geometry.)