document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442712>Question 442712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16x^2 + 9y^2 - 32x + 18y + 9 = 128\r<BR>\n" );
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document.write( "how do you write in standard form, find foci, and asymptotes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305407 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=305407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 16x^2 + 9y^2 - 32x + 18y + 9 = 128 <BR>\n" );
document.write( "how do you write in standard form, find foci, and asymptotes<BR>\n" );
document.write( "..<BR>\n" );
document.write( "completing the squares<BR>\n" );
document.write( "16(x^2-2x+1)+9(y^2+2y+1)=128-9+16+9=144<BR>\n" );
document.write( "(x-1)^2/9+(y+1)^2/16=1<BR>\n" );
document.write( "This is an ellipse with center at (1,-1) and vertical major axis.<BR>\n" );
document.write( "Because it is an ellipse, asymptotes do no apply<BR>\n" );
document.write( "Standard form of an ellipse with vertical major axis:<BR>\n" );
document.write( "(y-k)^2/a^2+(x-h)^2/b^2=1< with (h,k) being the (x,y) coordinates of the center. (a>b)<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "center(1,-1)<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=4 (length of major axis)<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3 (length of minor axis)<BR>\n" );
document.write( "c^2=a^2-b^2=16-9=7<BR>\n" );
document.write( "c=&#8730;7=2.65 (distance from ctr to foci on major axis.<BR>\n" );
document.write( "foci(1,-1+-2.65)<BR>\n" );
document.write( "see graph of the ellipse below<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=((1-(x-1)^2/9))*16))^.5-1<BR>\n" );
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