document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315531>Question 315531</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this question:<BR>\n" );
document.write( "y^2+2y=x^2+x<BR>\n" );
document.write( " is this equation a parabola, circle, ellipse, or hyperbola? how do you know?<BR>\n" );
document.write( "thnks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225746 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=225746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y^2+2y=x^2+x<BR>\n" );
document.write( "is this equation a parabola, circle, ellipse, or hyperbola? how do you know?<BR>\n" );
document.write( "It is a hypobola because the x^2 and y^2  have opposite signs when <BR>\n" );
document.write( "arranged on the same side of the equation.<BR>\n" );
document.write( "=================================================<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "x^2 + x - (y^2+2y) = 0<BR>\n" );
document.write( "Complete the square:<BR>\n" );
document.write( "(x^2 + x + (1/2)^2) - (y^2+2y+1) = (1/2)^2 - 1<BR>\n" );
document.write( "(x+1/2)^2 - (y+1)^2 = -3/4<BR>\n" );
document.write( "----<BR>\n" );
document.write( "(y+1)^2 - (x+(1/2))^2 = (3/4)<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============================== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );