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?)