Question 1209794
First, I'll generate some data for plotting the graph.
```python?code_reference&code_event_index=3
import pandas as pd
import numpy as np

# Generate x values from -7 to -1 with a step of 0.1
x = np.arange(-7, -1, 0.1)

# Calculate y values for the positive and negative square roots
y_pos = -3 + 2 * np.sqrt(1 - (x + 4)**2 / 9)
y_neg = -3 - 2 * np.sqrt(1 - (x + 4)**2 / 9)

# Combine x and y values into a DataFrame
df = pd.DataFrame({'x': np.concatenate((x, x)), 'y': np.concatenate((y_pos, y_neg))})

# Display the first 5 rows
print(df.head().to_markdown(index=False, numalign="left", stralign="left"))

# Print the column names and their data types
print(df.info())
```
```text?code_stdout&code_event_index=3
| x    | y        |
|:-----|:---------|
| -7   | -3       |
| -6.9 | -2.48792 |
| -6.8 | -2.28198 |
| -6.7 | -2.12822 |
| -6.6 | -2.00222 |
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 120 entries, 0 to 119
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       120 non-null    float64
 1   y       120 non-null    float64
dtypes: float64(2)
memory usage: 2.0 KB
None

```
Now, I'll use the generated data to plot the graph.
```python?code_reference&code_event_index=7
import altair as alt

# Create the Altair plot
chart = alt.Chart(df).mark_circle().encode(
    x=alt.X('x', title='x'),  # Set x-axis title
    y=alt.Y('y', title='y'),  # Set y-axis title
    tooltip=['x', 'y']  # Add tooltips for interactivity
).properties(
    title='Graph of (x+4)^2/9 + (y+3)^2/4 = 1'  # Set plot title
).interactive()  # Enable zooming and panning

# Save the plot
chart.save('graph_plot.json')
```

[json-tag: code-generated-json-0-1741108966998394562]

Here is the graph of the given equation $(x+4)^2/9+(y+3)^2 /4 =1$.

Let me know if you'd like to explore more about this equation or need further assistance with plotting other graphs.