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    rb23's Avatar
    rb23 Posts: 6, Reputation: 1
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    #1

    Mar 30, 2010, 12:31 PM
    Usage of Partial Differentiation...
    Does there exist any particular way of finding the centre of an ellipse by partially differentiating the equation with respect to x and y both and then finding the point of intersection??

    I'm asking this because I know it works for hyperbolas and due to symmetry in their relations I would like to know whether it works for ellipses too...
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Mar 31, 2010, 11:28 PM

    This should work according to me.

    If you get the equation of the normals at the various points, two would be enough, you should get your centre of elipse for a regular elipse with major axis and minor axis parallel to the x or y axes.

    If you have a 'slant' elipse, you can differentiate for gradient = 0 and infinite to get the points you need, then you get the line passing through them and their intersection will be the centre.
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