Question

In the following exercises, graph each ellipse.

$\frac{x^2}{25}+\frac{y^2}{9}=1.$

Short answer

The Graph of the given ellipse is given by

Step-by-step solution

Step 1.Given information

The equation of the ellipse is$\frac{x^2}{25}+\frac{y^2}{9}=1$

Step 2.  Concept used

The standard form of the ellipse

with Center at the origin 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

$\frac{x^2}{25}+\frac{y^2}{9}=1$

Compare the given equation with the standard form of the ellipse

$$\begin{gathered} \text{Center:(0,0),} \\ 36>25\text{and} \\ {a}^2=25\Rightarrow a=\pm 5 \\ {b}^2=9\Rightarrow b=\pm 3 \end{gathered}$$

Major axis:

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

Minor axis

On $y-$axis with endpoints$(0,-3),(0,3).$

Step 4. Sketch the ellipse

The graph of the ellipse is shown below