Find the Properties ((x+2)^2)/9+(y^2)/16=1

Simplify each term in the equation in order to set the right side equal to ${\displaystyle 1}$. The standard form of an ellipse or hyperbola requires the right side of the equation be ${\displaystyle 1}$.

This is the form of an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.

Match the values in this ellipse to those of the standard form. The variable ${\displaystyle a}$ represents the radius of the major axis of the ellipse, ${\displaystyle b}$ represents the radius of the minor axis of the ellipse, ${\displaystyle h}$ represents the x-offset from the origin, and ${\displaystyle k}$ represents the y-offset from the origin.

The center of an ellipse follows the form of ${\displaystyle (h,k)}$. Substitute in the values of ${\displaystyle h}$ and ${\displaystyle k}$.

These values represent the important values for graphing and analyzing an ellipse.

Center: ${\displaystyle (-2,0)}$

${\displaystyle {\text{Vertex}}_1}$: ${\displaystyle (-2,4)}$

${\displaystyle {\text{Vertex}}_2}$: ${\displaystyle (-2,-4)}$

${\displaystyle {\text{Focus}}_1}$: ${\displaystyle (-2,\sqrt{7})}$

${\displaystyle {\text{Focus}}_2}$: ${\displaystyle (-2,-\sqrt{7})}$

Eccentricity: ${\displaystyle \frac{\sqrt{7}}{4}}$