Question

identify the graph of $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$.

Explanation:

Step1: Recall the standard form of an ellipse

The standard - form of an ellipse centered at the origin is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1$, where $a$ and $b$ are the semi - major and semi - minor axes respectively. The given equation is $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$, so $a^{2}=36$ (i.e., $a = 6$) and $b^{2}=16$ (i.e., $b = 4$).

Step2: Analyze the shape of the ellipse

Since $a>b$, the major axis of the ellipse is along the $x$ - axis.

Answer:

D.