https://file.aiquickdraw.com/mathbot/file/1726403174298gl806bd7.jpg

To solve this problem, we need to identify the equation of the ellipse based on the graph.

### Standard Equation of an Ellipse:
The equation of an ellipse centered at the origin \((0,0)\) is given by:

\[
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1
\]

Where:
- \(a\) is the semi-major axis (the distance from the center to the farthest point on the ellipse along the x-axis or y-axis).
- \(b\) is the semi-minor axis (the distance from the center to the shortest point on the ellipse along the x-axis or y-axis).

### Step-by-Step Solution:
1. **Identify the Semi-Major and Semi-Minor Axes:**
   - From the graph, the ellipse is wider along the x-axis. This means the major axis is along the x-axis, and the semi-major axis length is \(a = 4\).
   - The minor axis is along the y-axis, and the semi-minor axis length is \(b = 3\).

2. **Write the Equation:**
   - Using the values \(a = 4\) and \(b = 3\), the equation of the ellipse is:

\[
\frac{x^2}{4^2} + \frac{y^2}{3^2} = 1
\]

Which simplifies to:

\[
\frac{x^2}{16} + \frac{y^2}{9} = 1
\]

### Answer:
The correct equation of the ellipse is:

\[
\frac{x^2}{16} + \frac{y^2}{9} = 1
\]

Thus, the first option highlighted is correct.

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Would you like further explanation on ellipses or their properties?

Here are some related questions:
1. How can we differentiate between an ellipse and a circle graphically?
2. What happens if the semi-major axis is along the y-axis instead?
3. How do you calculate the foci of an ellipse?
4. Can an ellipse equation have a center other than the origin?
5. What changes in the equation if we rotate the ellipse?

**Tip:** For ellipses, always check which axis (x or y) is longer to identify the semi-major and semi-minor axes.

What is the equation of the ellipse whose graph is given below?

Learn how to determine the equation of an ellipse from its graph. This problem covers key concepts in analytic geometry and conic sections, focusing on ellipses. Suitable for high school students.

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