Conic Rotation 3: half-axes

[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. _____ 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)

 

Ryan Hirst

 
Resource Type
Activity
Tags
classical  conic  geometry  rotation  sections 
Target Group (Age)
19+
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English (United States)
 
 
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4.2
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