Standard Forms of Equations for Ellipses Centered at (0,0)

Horizontal Ellipse

The ellipse with center at the origin and equation $LaTeX: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ (where LaTeX: a>b $a>b$ ) has vertices $LaTeX: \left(\pm a,0\right)$ $\left(\pm a,0\right)$ , endpoints of the minor axis $LaTeX: \left(0,\pm b\right)$ $\left(0,\pm b\right)$ , and foci $LaTeX: \left(\pm c,0\right)$ $\left(\pm c,0\right)$ , where LaTeX: c^2=a^2-b^2 $c^2=a^2-b^2$ .

Horizontal Ellipse Centered at (0,0).PNG

Vertical Ellipse

The ellipse with center at the origin and equation $LaTeX: \frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ (where LaTeX: a>b $a>b$ ) has vertices $LaTeX: \:\left(0,\pm a\right),\:$ $\:\left(0,\pm a\right),\:$ endpoints of the minor axis $LaTeX: \:\left(\pm b,0\right),\:$ $\:\left(\pm b,0\right),\:$ and foci $LaTeX: \:\left(0,\pm c\right),\:$ $\:\left(0,\pm c\right),\:$ where LaTeX: c^2=a^2-b^2. $c^2=a^2-b^2.$

Vertical Ellipse with Center (0,0).PNG