Propositions:
Given an equation in the form, Ax²+ Bxy+Cy² = ±1, to determine
*the angle of rotation, θ smoothly in the range -π/2 ≤θ ≤ π/2. (Disambiguate limit cases).
*the half-axis lengths a, b and their relative orientation.
Method: Geometric construction of the tangent ratio from the coefficients A, B, C.
Step-by-step with Construction Protocol.
Take a look. It's pretty.
_____
Conic Rotation
1. Ellipse, 1: Conversion between the Standard Form and parametric equations: http://www.geogebratube.org/material/show/id/45277
2. Ellipse, 2: Resolving discontinuity under rotation. http://www.geogebratube.org/material/show/id/45026
*3. Determine the half-axis lengths and orientation, disambiguate tan(θ)
