Q1. Pick integers a, b > 0 and solve the corresponding hyperbolic equation
x2 - ax - b2 = 0
Q2. Explain why x = BC in Descartes construction for hyperbolic equations is a solution. (That is use algebra to PROVE x = BC is a solution of x2 - ax - b2 = 0. Definition of a circle, Pythagorean Theorem, and simple symbol shuffling should suffice.)
Q3. Pick integers a, b > 0 and solve the corresponding hyperbolic equation
x2 + ax - b2 = 0
using Descartes' method. Make a careful sketch and measure the solution on your sketch.
Q4. Pick integers a. b > 0, such that a/2 > b > 0 and solve the corresponding elliptic equation
x2 - ax + b2 = 0
using Descartes' method. Make a careful sketch and measure the solution on your sketch.
Q5. Explain why x = SB and x = AS in Descartes construction for elliptic equations solutions. (That is use algebra to PROVE x = SB and x = AS are solutions. As part of your solution be sure to explain why is ∠AQB a right angle?)