document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194051>Question 194051</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What shape does this equation make? (circle, ellipse, hyperbola) <BR>\n" );
document.write( "4x^2 + 16x + y^2 - 6y = -21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145654 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=145654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^2 + 16x      +y^2 -6y    =  -21<BR>\n" );
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document.write( "if  we  complete  the  squares,  we  can  see  form  <BR>\n" );
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document.write( "4 (x^2 +4x +4)    +y^2 -6y  +9  =  -21  +16  +9,,,,(4*4=16)<BR>\n" );
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document.write( "remember  (4/2)^2 = 4  and   (-6/2)^2  =9,,,,   and  add to  both  sides  to  balance<BR>\n" );
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document.write( "4(x+2)^2  +  (y-3)^2  = 4<BR>\n" );
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document.write( "divide  thru  by  4<BR>\n" );
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document.write( "((x+2)^2)/1 +(  (y-3)^2 )/4=4/4=1<BR>\n" );
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document.write( "the  form for  ellipse  is,  x^2/a^2  +y^2/b^2  =1<BR>\n" );
document.write( "therefore  it  fits  an  ellipse </SPAN>\n" );
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