document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190882>Question 1190882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the ELLIPSE that satisfies the given conditions \r<BR>\n" );
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document.write( "c. Center at (0, 0) one vertex (0, - 6) end of the minor axis (4,0)\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 #849193 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=849193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to determine the equation of the ellipse:\r<BR>\n" );
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document.write( "**1. Identify the Center:**\r<BR>\n" );
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document.write( "The center is given as (0, 0).\r<BR>\n" );
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document.write( "**2. Determine the Orientation:**\r<BR>\n" );
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document.write( "Since a vertex is at (0, -6), which lies directly below the center, the major axis is vertical.\r<BR>\n" );
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document.write( "**3. Find 'a' (Semi-major Axis):**\r<BR>\n" );
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document.write( "The distance from the center (0, 0) to the vertex (0, -6) is 6 units.  Therefore, a = 6.\r<BR>\n" );
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document.write( "**4. Find 'b' (Semi-minor Axis):**\r<BR>\n" );
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document.write( "The end of the minor axis is at (4, 0). The distance from the center (0, 0) to this point is 4 units. Therefore, b = 4.\r<BR>\n" );
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document.write( "**5. Write the Equation:**\r<BR>\n" );
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document.write( "The general equation of an ellipse centered at (h, k) with a vertical major axis is:\r<BR>\n" );
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document.write( "(x - h)² / b² + (y - k)² / a² = 1\r<BR>\n" );
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document.write( "Substitute the values we found (h = 0, k = 0, a = 6, b = 4):\r<BR>\n" );
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document.write( "(x - 0)² / 4² + (y - 0)² / 6² = 1\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "x² / 16 + y² / 36 = 1\r<BR>\n" );
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document.write( "Therefore, the equation of the ellipse is x²/16 + y²/36 = 1.<BR>\n" );
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