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September 20th, 2007, 08:46 PM   #1
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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!

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September 21st, 2007, 04:29 AM   #2
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For one thing, you'll need to use parametric equations, since a nondegenerate rotated ellipse isn't a function.
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September 21st, 2007, 06:06 AM   #3
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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.

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