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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... |
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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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