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September 20th, 2007, 08:46 PM  #1 
Newbie Joined: Sep 2007 Posts: 2 Thanks: 0  Rotating an ellipse around an arbitrary point
Suppose I have the equation for an ellipse ... say for example, x^2/9 + y^2/16 = 1 ... and I want to rotate it (in the plane) around a point such as (2,2). How do I represent the equation for the rotated ellipse? More generally, if I have any equation for an ellipse, possibly one that has even been translated up or down, and right or left, and I want to rotate it about any given point ... how do I represent the rotated ellipse? Thanks! This one is driving me nuts! John 
September 21st, 2007, 04:29 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
For one thing, you'll need to use parametric equations, since a nondegenerate rotated ellipse isn't a function.

September 21st, 2007, 06:06 AM  #3 
Newbie Joined: Sep 2007 Posts: 2 Thanks: 0 
True. That's why I said I had an equation. For a standard ellipse, I would just use the standard form (x^2)/(a^2) + (y^2)/(b^2) = 1 Rotating this some arbitrary amount, like 37 degrees, would just look like a slanted ellipse. The equation for that however is still eluding me. John 

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