The foci and rotation angle of an ellipse, $E_0$, as a function of the coefficients of an equation of $E_0$

Abstract

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 $E_0$.