Question

In the following exercises, graph each ellipse.

$9x^2+25y^2=225$

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 $9x^2+25y^2=225$

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. Convert into standard form 

$$\begin{gathered} 9x^2+25y^2=225\text{Given} \\ \frac{9x^2}{225}+\frac{25y^2}{225}=\frac{225}{225}\text{Dividewith225onbothsides} \\ \frac{x^2}{25}+\frac{y^2}{9}=1\text{Simplify} \end{gathered}$$

Step 4.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

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

Major axis:

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

Minor axis

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

Step 5. Sketch the graph

The graph of the ellipse is