document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190881>Question 1190881</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( "b. Vertices (-1.3) and (5, 3) length of minor axis 4\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 #849194 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=849194\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the equation of the ellipse:\r<BR>\n" );
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document.write( "1. **Find the Center:** The center of the ellipse is the midpoint of the line segment connecting the vertices.  The midpoint formula is ((x₁ + x₂)/2, (y₁ + y₂)/2).\r<BR>\n" );
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document.write( "   Center = ((-1 + 5)/2, (3 + 3)/2) = (2, 3)\r<BR>\n" );
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document.write( "2. **Determine the Orientation:** Since the vertices have the same y-coordinate, the major axis is horizontal.\r<BR>\n" );
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document.write( "3. **Find 'a' (Semi-major Axis):** The semi-major axis is the distance from the center to a vertex.\r<BR>\n" );
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document.write( "   a = distance from (2, 3) to (5, 3) = |5 - 2| = 3\r<BR>\n" );
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document.write( "4. **Find 'b' (Semi-minor Axis):** The length of the minor axis is given as 4. The semi-minor axis is half of this length.\r<BR>\n" );
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document.write( "   b = 4 / 2 = 2\r<BR>\n" );
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document.write( "5. **Write the Equation:** The general equation of an ellipse centered at (h, k) with a horizontal major axis is:\r<BR>\n" );
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document.write( "   (x - h)² / a² + (y - k)² / b² = 1\r<BR>\n" );
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document.write( "   Substitute the values we found (h = 2, k = 3, a = 3, b = 2):\r<BR>\n" );
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document.write( "   (x - 2)² / 3² + (y - 3)² / 2² = 1\r<BR>\n" );
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document.write( "   Simplify:\r<BR>\n" );
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document.write( "   (x - 2)² / 9 + (y - 3)² / 4 = 1\r<BR>\n" );
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document.write( "Therefore, the equation of the ellipse is (x - 2)²/9 + (y - 3)²/4 = 1.<BR>\n" );
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