An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance of 2c is a given positive constant 2a (Hilbert and Cohn-Vossen 1999, p. 2).

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An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance of 2c is a given positive constant 2a (Hilbert and Cohn-Vossen 1999, p. 2).

`Ellipse Formulas`

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An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance of 2c is a given positive constant 2a (Hilbert and Cohn-Vossen 1999, p. 2).

$A$, Symbol for Area;

${a}_{}$, The length of semi-major axis;

${b}_{}$, The length of semi-minor axis;

$A=\mathrm{\pi ab}$

$\mathrm{c}=\sqrt{{\mathrm{a}}^{2}-{\mathrm{b}}^{2}}$

$\frac{(x-{x}_{0}{)}^{2}}{{a}^{2}}+\frac{(y-{y}_{0}{)}^{2}}{{b}^{2}}=1$

^{Figure - 25.1} http://xahlee.info/SpecialPlaneCurves_dir/Ellipse_dir/ellipse.png