document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141095>Question 141095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to Identify the conic section, then  place in standard form. The equation is: 4x^2+y^2+8x-4y-28=0\r<BR>\n" );
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document.write( "This is as far as i have been able to solve it. \r<BR>\n" );
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document.write( "(4x^2+8x)+(y^2-4y)=28<BR>\n" );
document.write( "[4(x+1)^2-1]+(y-2)^2-4=28<BR>\n" );
document.write( "                    +4 +4<BR>\n" );
document.write( "4(x+1)^2+(y-2)^2-1=32<BR>\n" );
document.write( "                +1 +1<BR>\n" );
document.write( "4(x+1)^2/33+(y-4)^2/33=1\r<BR>\n" );
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document.write( "any help you can give would be wonderful. Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102775 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=102775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^2+y^2+8x-4y-28=0 \r<BR>\n" );
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document.write( "Sort it out and factor the coefficient of x^2.  Leave spaces in order to complete the square in the next steps:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+%2B8x+%2B_____%2By%5E2+-4y+%2B+_____+=+28 ALIGN=MIDDLE  ALT=\"4x%5E2+%2B8x+%2B_____%2By%5E2+-4y+%2B+_____+=+28\"   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=4%28x%5E2+%2B2x+%2B_____%29%2By%5E2+-4y+%2B+_____+=+28+%2B+_____+%2B+_____ ALIGN=MIDDLE  ALT=\"4%28x%5E2+%2B2x+%2B_____%29%2By%5E2+-4y+%2B+_____+=+28+%2B+_____+%2B+_____\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To complete the square, you must take half of the x coefficient (Half of 2 is 1, and square which is 1.  On the right side, however, you must add 4*1 which is 4.  It should look like this: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2+%2B2x+%2B_____%29%2By%5E2+-4y+%2B+_____+=+28+%2B+_____+%2B+_____ ALIGN=MIDDLE  ALT=\"4%28x%5E2+%2B2x+%2B_____%29%2By%5E2+-4y+%2B+_____+=+28+%2B+_____+%2B+_____\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2+%2B2x+%2B1++%29%2By%5E2+-4y+%2B+4+=+28+%2B+4%2A1+%2B+4 ALIGN=MIDDLE  ALT=\"4%28x%5E2+%2B2x+%2B1++%29%2By%5E2+-4y+%2B+4+=+28+%2B+4%2A1+%2B+4\"   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=4%28x%2B1%29%5E2+%2B+%28y-2%29%5E2+=+36+ ALIGN=MIDDLE  ALT=\"4%28x%2B1%29%5E2+%2B+%28y-2%29%5E2+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by 36 to write this in standard form for an ellipse:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B1%29%5E2+%2B+%28y-2%29%5E2+=+36+ ALIGN=MIDDLE  ALT=\"4%28x%2B1%29%5E2+%2B+%28y-2%29%5E2+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28x%2B1%29%5E2%29%2F36+%2B+%28%28y-2%29%5E2%29%2F36+=+36%2F36+ ALIGN=MIDDLE  ALT=\"%284%28x%2B1%29%5E2%29%2F36+%2B+%28%28y-2%29%5E2%29%2F36+=+36%2F36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B1%29%5E2%29%2F9+%2B+%28%28y-2%29%5E2%29%2F36+=+1+ ALIGN=MIDDLE  ALT=\"%28%28x%2B1%29%5E2%29%2F9+%2B+%28%28y-2%29%5E2%29%2F36+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is an ellipse, with center at (-1,2), with a \"radius\" of 3 in the x direction, and a \"radius\" of 6 in the y direction.\r<BR>\n" );
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document.write( "R^2 </SPAN>\n" );
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