document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209794>Question 1209794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+4)^2/9+(y+3)^2 /4 =1\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850489 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, I'll generate some data for plotting the graph.<BR>\n" );
document.write( "```python?code_reference&code_event_index=3<BR>\n" );
document.write( "import pandas as pd<BR>\n" );
document.write( "import numpy as np\r<BR>\n" );
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document.write( "# Generate x values from -7 to -1 with a step of 0.1<BR>\n" );
document.write( "x = np.arange(-7, -1, 0.1)\r<BR>\n" );
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document.write( "# Calculate y values for the positive and negative square roots<BR>\n" );
document.write( "y_pos = -3 + 2 * np.sqrt(1 - (x + 4)**2 / 9)<BR>\n" );
document.write( "y_neg = -3 - 2 * np.sqrt(1 - (x + 4)**2 / 9)\r<BR>\n" );
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document.write( "# Combine x and y values into a DataFrame<BR>\n" );
document.write( "df = pd.DataFrame({'x': np.concatenate((x, x)), 'y': np.concatenate((y_pos, y_neg))})\r<BR>\n" );
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document.write( "# Display the first 5 rows<BR>\n" );
document.write( "print(df.head().to_markdown(index=False, numalign=\"left\", stralign=\"left\"))\r<BR>\n" );
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document.write( "# Print the column names and their data types<BR>\n" );
document.write( "print(df.info())<BR>\n" );
document.write( "```<BR>\n" );
document.write( "```text?code_stdout&code_event_index=3<BR>\n" );
document.write( "| x    | y        |<BR>\n" );
document.write( "|:-----|:---------|<BR>\n" );
document.write( "| -7   | -3       |<BR>\n" );
document.write( "| -6.9 | -2.48792 |<BR>\n" );
document.write( "| -6.8 | -2.28198 |<BR>\n" );
document.write( "| -6.7 | -2.12822 |<BR>\n" );
document.write( "| -6.6 | -2.00222 |<BR>\n" );
document.write( "<class 'pandas.core.frame.DataFrame'><BR>\n" );
document.write( "RangeIndex: 120 entries, 0 to 119<BR>\n" );
document.write( "Data columns (total 2 columns):<BR>\n" );
document.write( " #   Column  Non-Null Count  Dtype  <BR>\n" );
document.write( "---  ------  --------------  -----  <BR>\n" );
document.write( " 0   x       120 non-null    float64<BR>\n" );
document.write( " 1   y       120 non-null    float64<BR>\n" );
document.write( "dtypes: float64(2)<BR>\n" );
document.write( "memory usage: 2.0 KB<BR>\n" );
document.write( "None\r<BR>\n" );
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document.write( "```<BR>\n" );
document.write( "Now, I'll use the generated data to plot the graph.<BR>\n" );
document.write( "```python?code_reference&code_event_index=7<BR>\n" );
document.write( "import altair as alt\r<BR>\n" );
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document.write( "# Create the Altair plot<BR>\n" );
document.write( "chart = alt.Chart(df).mark_circle().encode(<BR>\n" );
document.write( "    x=alt.X('x', title='x'),  # Set x-axis title<BR>\n" );
document.write( "    y=alt.Y('y', title='y'),  # Set y-axis title<BR>\n" );
document.write( "    tooltip=['x', 'y']  # Add tooltips for interactivity<BR>\n" );
document.write( ").properties(<BR>\n" );
document.write( "    title='Graph of (x+4)^2/9 + (y+3)^2/4 = 1'  # Set plot title<BR>\n" );
document.write( ").interactive()  # Enable zooming and panning\r<BR>\n" );
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document.write( "# Save the plot<BR>\n" );
document.write( "chart.save('graph_plot.json')<BR>\n" );
document.write( "```\r<BR>\n" );
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document.write( "[json-tag: code-generated-json-0-1741108966998394562]\r<BR>\n" );
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document.write( "Here is the graph of the given equation $(x+4)^2/9+(y+3)^2 /4 =1$.\r<BR>\n" );
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document.write( "Let me know if you'd like to explore more about this equation or need further assistance with plotting other graphs. </SPAN>\n" );
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