document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118267>Question 118267</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you write this equation of ellipse in simple form?\r<BR>\n" );
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document.write( "3x^2 + 4y^2 + 8y=8 <BR>\n" );
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document.write( "  * I tried dividing everything by eigth leaving me with:\r<BR>\n" );
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document.write( "       3x^2/8 +y^2/2 + y=1<BR>\n" );
document.write( "    But when i checked to see if i had the right answer i got it wrong this is the correct answer:<BR>\n" );
document.write( "      x^2/4 + (y+1)^2/3=1\r<BR>\n" );
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document.write( "    I don't understand why i got the problem wrong.<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 #86386 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86386\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard form for the equation of an ellipse with center at (h, k) and major axis parallel to the x-axis is: (a is the semi-major axis and b is the semiminor axis)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or, if the major axis is parallel to the y-axis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Starting with the given equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B4y%5E2%2B8y+=+8 ALIGN=MIDDLE  ALT=\"3x%5E2%2B4y%5E2%2B8y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the terms as shown:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%29%2B%284y%5E2%2B8y%29+=+8 ALIGN=MIDDLE  ALT=\"%283x%5E2%29%2B%284y%5E2%2B8y%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor a 4 from the y-group.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%29%2B4%28y%5E2%2B2y%29+=+8 ALIGN=MIDDLE  ALT=\"%283x%5E2%29%2B4%28y%5E2%2B2y%29+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now complete the square in the y-terms inside the parentheses by adding the square of half the y-coefficient or (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F2%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%282%2F2%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), remembering that you are really adding 4 because of the 4 in front of the parentheses.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%29%2B4%28y%5E2%2B2y%2B1%29+=+8%2B4 ALIGN=MIDDLE  ALT=\"%283x%5E2%29%2B4%28y%5E2%2B2y%2B1%29+=+8%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now simplify this by factoring the trinomial in the y-terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%29%2B4%28y%2B1%29%5E2+=+12 ALIGN=MIDDLE  ALT=\"%283x%5E2%29%2B4%28y%2B1%29%5E2+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide through by 12 to get the right side equal to 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F12%29x%5E2+%2B+%284%2F12%29%28y%2B1%29%5E2+=+12%2F12 ALIGN=MIDDLE  ALT=\"%283%2F12%29x%5E2+%2B+%284%2F12%29%28y%2B1%29%5E2+=+12%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4+%2B+%28y%2B1%29%5E2%2F3+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4+%2B+%28y%2B1%29%5E2%2F3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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