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We have major axis, minor axis and the phi between major axis and y axis in a rotated ellipse. How can we find the maximum y?

Ali
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  • And the phi that y become maximum – Ali May 25 '13 at 14:29
  • What background do you have? If you rotate your question, you're asking for a point on a "standard" ellipse where the tangent line is perpendicular to the line $y=(\tan\phi)x$ ... – Ted Shifrin May 25 '13 at 20:02

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It's easy to see that $\phi=0$ gives the maximum $y$. If you think vectorially, the position vector in direction of the major axis is longest. If you take a different vector and then project it, it gets shorter and shorter again.

Ted Shifrin
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  • Dear Ted, IT is not correct. see the following link and the picture.http://math.stackexchange.com/questions/91132/how-to-get-the-limits-of-rotated-ellipse – Ali May 26 '13 at 04:48
  • Background: I have a elliptical orbit for a rotating shaft that shows the position of the rotor center at one turn. I have the phase that rotor is farthest from the center (a,b, phi). But I want to find the phase in which the y become maximum to use it for balancing the rotor (finding influence coefficients of the rotor). Because the sensor in located in the y direction. – Ali May 26 '13 at 05:09
  • What I've said is correct if everything is 2-dimensional. But your description here sounds like you're thinking 3-dimensionally. – Ted Shifrin May 26 '13 at 18:40