### Assignment #7

**Due: 8 February,1999**

**1.** Once again, the good ship *Swine Trek* is forced to save two-dimensional space: the Cylons have launched a failing mark in MA 110 along the positive y-axis, straight at the origin. Ivanova orders the ship to move along the x-axis so as to cross the path of the mark 10 units ahead of it and lock on with a tractor beam. The *Swine Trek's* tractor beam subsequently keeps the mark at a constant distance of 10 units from the ship while the ship continues to move along the positive x-axis. Phaicus observes that the path of the mark is always tangent to the tractor beam and finds an equation in x and y describing the path of the mark after the *Swine Trek* starts towing it. Find this equation! *[7]*
**2.** As you probably figured out on the last assignment, the Fibonacci numbers are given by the relations f_{1} = 1, f_{2} = 1, and f_{n+2} = f_{n+1} + f_{n} for n > 0. Prove that

**Bonus:** Which four science-fiction TV shows are referenced in Problem **1**}? *[0.4]*

Department of Mathematics
Trent University

Maintained by Stefan Bilaniuk. Last updated 1999.12.03.