Deriving the Equation of a Hyperbola using CAS and Why c^2 = a^2 + b^2

In this video we use the TI-Nspire CX CAS's computer algebra system to work from the definition of a hyperbola to the standard form of the equation of a hyperbola. In the process we see why, algebraically, c^2 = a^2 + b^2. We also see why the constant difference is equal to 2a, twice the distance from the center to a vertex. There's a lot of functions being used on the TI-Nspire CAS. We use expand often and also the built-in right() function, which returns the right hand side of an equation. I'm sure people still derive the equations of conic sections by hand, but this is the kind of thing where a CAS really makes a difference with no loss of learning.