[b]Propositions:[/b]
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.
[i]Method:[/i] Geometric construction of the tangent ratio from the coefficients A, B, C.
Step-by-step with Construction Protocol.
Take a look. It's pretty.
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Conic Rotation
1. Ellipse, 1: Conversion between the Standard Form and parametric equations: [url]http://www.geogebratube.org/material/show/id/45277[/url]
2. Ellipse, 2: Resolving discontinuity under rotation. [url]http://www.geogebratube.org/material/show/id/45026[/url]
*3. Determine the half-axis lengths and orientation, disambiguate tan(θ)
