document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=435959>Question 435959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me do this problem, graph it, and figure out what it would be. My choices of what it could be are ellipse, circle, parabola, and hyperbola.  9x^2+36y^2-72x-180  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302004 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=302004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please help me do this problem, graph it, and figure out what it would be. My choices of what it could be are ellipse, circle, parabola, and hyperbola. 9x^2+36y^2-72x-180<BR>\n" );
document.write( "..<BR>\n" );
document.write( "9x^2+36y^2-72x-180<BR>\n" );
document.write( "For an expression to be an equation, it must be equal to some number. I will assume the given expression is equal to zero.<BR>\n" );
document.write( "9x^2+36y^2-72x-180=0<BR>\n" );
document.write( "9x^2+36y^2-72x=180<BR>\n" );
document.write( "completing the squares<BR>\n" );
document.write( "9(x^2-8x+16)+36y^2=180-144=36<BR>\n" );
document.write( "9(x-4)^2+36y^2=36<BR>\n" );
document.write( "divide by 36<BR>\n" );
document.write( "(x-4)^2/4+y^2/1=1<BR>\n" );
document.write( "Standard form for an ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b)<BR>\n" );
document.write( "with (h,k) being the (x,y) coordinates of the center<BR>\n" );
document.write( "At you can see this is an ellipse with center at (4,0) with a horizontal major axis<BR>\n" );
document.write( "Also:<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "See the graph below:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=+-(1-(x-4)^2/4)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+10%2C+-5%2C+4%2C+%281-%28x-4%29%5E2%2F4%29%5E.5%2C-%281-%28x-4%29%5E2%2F4%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );