Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The foci and rotation angle of an ellipse, $E_0$, as a function of the
  coefficients of an equation of $E_0$   First, we give a formula for the foci of an ellipse, $E_0$, as a function of
the coefficients of an equation of $E_0$(see Theorem <ref>T2</ref>). To prove
Theorem <ref>T2</ref>, we use two interesting formulas proven in <cite>B</cite>
and in <cite>S</cite>. Our second result(see Theorem <ref>T3</ref>), is a more
precise formula for the rotation angle of $E_0$ as a function of the
coefficients of an equation of $E_0$.

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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg