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For the general form of the equation the coefficient ''A'' is the height of the peak and {{math|(''x''<sub>0</sub>, ''y''<sub>0</sub>)}} is the center of the blob.
If we set
<math display="block"> \begin{align}
a &= \frac{\cos^2\theta}{2\sigma_X^2} + \frac{\sin^2\theta}{2\sigma_Y^2}, \\
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\end{align}
</math>then we rotate the blob by a positive, counter-clockwise angle <math>\theta</math> (for negative, clockwise rotation, invert the signs in the ''b'' coefficient).<ref>{{cite web |last1=Nawri |first1=Nikolai |title=Berechnung von Kovarianzellipsen |url=http://imkbemu.physik.uni-karlsruhe.de/~eisatlas/covariance_ellipses.pdf |access-date=14 August 2019 |url-status=dead |archive-url=https://web.archive.org/web/20190814081830/http://imkbemu.physik.uni-karlsruhe.de/~eisatlas/covariance_ellipses.pdf |archive-date=2019-08-14}}</ref>
To get back the coefficients <math>\theta</math>, <math>\sigma_X</math> and <math>\sigma_Y</math> from <math>a</math>, <math>b</math> and <math>c</math> use
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