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 #86384 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=86384\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4y%5E2+%2B+8y=8 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4y%5E2+%2B+8y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4%28y%5E2+%2B+2y%29=8 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4%28y%5E2+%2B+2y%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out 4 from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2+%2B+8y ALIGN=MIDDLE  ALT=\"4y%5E2+%2B+8y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28y%5E2+%2B+2y%29 ALIGN=MIDDLE  ALT=\"4%28y%5E2+%2B+2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4%28y%5E2+%2B+2y%2B1-1%29=8 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4%28y%5E2+%2B+2y%2B1-1%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the \"y\" coefficient 2 to get 1. Now square 1 to get 1. Add this and it's opposite -1 inside the parenthesis. Notice how 1-1=0 so it does not change the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4%28%28y%2B1%29%5E2-1%29=8 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4%28%28y%2B1%29%5E2-1%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2B+2y%2B1 ALIGN=MIDDLE  ALT=\"y%5E2+%2B+2y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4%28y%2B1%29%5E2-4=8 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4%28y%2B1%29%5E2-4=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4%28y%2B1%29%5E2%2Bcross%28-4%2B4%29=8%2B4 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4%28y%2B1%29%5E2%2Bcross%28-4%2B4%29=8%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 4 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4%28y%2B1%29%5E2=12 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4%28y%2B1%29%5E2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2+%2B+4%28y%2B1%29%5E2%29%2F12=cross%2812%2F12%29 ALIGN=MIDDLE  ALT=\"%283x%5E2+%2B+4%28y%2B1%29%5E2%29%2F12=cross%2812%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now Divide both sides by 12 to get the right side equal to one. With any ellipse, we always want the right side equal to one.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E2%29%2F12+%2B+%284%28y%2B1%29%5E2%29%2F12=1 ALIGN=MIDDLE  ALT=\"%283x%5E2%29%2F12+%2B+%284%28y%2B1%29%5E2%29%2F12=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F4+%2B+%28y%2B1%29%5E2%2F3=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F4+%2B+%28y%2B1%29%5E2%2F3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the ellipse in standard form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F4+%2B+%28y%2B1%29%5E2%2F3=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F4+%2B+%28y%2B1%29%5E2%2F3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Remember, we are trying to go from something like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BCy%5E2%2BDy%2BE=F ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BCy%5E2%2BDy%2BE=F\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <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;\" >. Looking at your answer, notice how you have an extra \"y\" which does not fit the standard equation of an ellipse. This is why you must complete the square to get the equation to fit the form. Does that make sense? </SPAN>\n" );
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