Question

In the following exercises, graph each ellipse.
$\frac{x^2}{16}+\frac{y^2}{36}=1.$

Short answer

The graph of the ellipse is

Step-by-step solution

Step 1. Given information

The equation of the ellipse is$\frac{x^2}{16}+\frac{y^2}{36}=1.$

Step 2. Concept used

The standard form of the ellipse with

$\text{Centre:}\left(0,0\right)\text{is}$

$$\begin{gathered} \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \\ a>b\Rightarrow \text{majoraxisis}x-\text{axiswithendpoints}\left(-a,0\right)\text{,(a,0)} \\ b>a\Rightarrow \text{majoraxisis}y-\text{axis.withendpoints}\left((0,-b\right)\text{,(0,b)} \end{gathered}$$

Step 3. Find the center and major axis

$\frac{x^2}{16}+\frac{y^2}{36}=1$

Compare with the standard form of the ellipse

localid="1645432640134" $$\begin{gathered} \text{Center}\left(0,0\right)\text{,} \\ 36>16\text{and} \\ {a}^2=16\Rightarrow a=\pm 4 \\ {b}^2=36\Rightarrow b=\pm 6 \end{gathered}$$

Major axis:

Onlocalid="1645425899245" $y-\text{axis}$with endpoints $(0,-6),(0,6).$

Minor axis:

Onlocalid="1645426041274" $x-\text{axiswithendpoints}\left(-4,0),(0,4\right)\text{.}$

Step 4. Graph the ellipse

The graph of the ellipse is