## Introduction

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 Calculator

## Introduction

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).

# Description

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;

## Area

$A=\mathrm{\pi ab}$

# Output

## The distance from the center to a focus(c)

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

# Output

## Ellipse The Given Point Test

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

# Output

## References

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