Question

In the following exercises, graph each ellipse.

$\frac{x^2}{25}+\frac{y^2}{36}=1.$

Short answer

The graph of the ellipse is

Step-by-step solution

Step 1. Given information

The equation of the ellipse is$\frac{x^2}{25}+\frac{y^2}{36}=1.$

Step 2. Concept used

The standard form of the ellipse

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

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

Step 3. Find the center and major axis

Compare the given equation with the standard form of the ellipse

$$\begin{gathered} \frac{x^2}{25}+\frac{y^2}{36}=1 \\ \text{Center:(0,0),} \\ 36>25\text{and} \\ {a}^2=25\Rightarrow a=\pm 5 \\ {b}^2=36\Rightarrow b=\pm 6 \end{gathered}$$

Major axis:

On $y-$axis with endpoints$(0,-6),(0,6).$

Minor axis:

On $x-$axis with endpoints$(-5,0),(5,0).$

Step 4. Sketch the graph

The graph of the given equation is