the graph shows an ellipse. write its equation in standard form.

Explanation:

Step1: Identify the center

The center of the ellipse is at the origin $(0,0)$ since it is symmetric about the x - axis and y - axis and centered at the intersection of the axes.

Step2: Find the semi - major and semi - minor axes

The ellipse intersects the x - axis at $x = 4$ and $x=-4$, so the semi - major axis $a = 4$ (assuming $a\geq b$). It intersects the y - axis at $y = 2$ and $y = - 2$, so the semi - minor axis $b=2$.

Step3: Write the standard form equation

The standard form of the equation of an ellipse centered at the origin $(h,k)=(0,0)$ is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1$. Substituting $a = 4$ and $b = 2$ into the equation, we get $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$.

Answer:

$\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$