[b]Proposition:[/b]
Given an ellipse rotated by ∡θ, determine the relationships among the values a, b, θ, and the equations
i) Ax² −2Bxy + Cy² = F
ii) x²/a² + y²/b² =1
iii) Parametric equation r(t) = a u + b v
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Ellipse Rotation, (1 of 3):
[b]→1: Converting between standard form and parametric equations.[/b]
2: Resolving discontinuities for the full range, 0 ≤ θ≤ 2π.
[url]http://www.geogebratube.org/material/show/id/45026[/url]
3. Determine the half-axis lengths and orientation, disambiguate tan(θ) for limit cases: [url]http://www.geogebratube.org/material/show/id/45924[/url]
