document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975420>Question 975420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the ellipse:   9x2 + 4y2 + 18x - 48y + 117 = 0           \r<BR>\n" );
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document.write( "     a) Put the equation in standard form             <BR>\n" );
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document.write( "     b) Horizontal or vertical major axis?            <BR>\n" );
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document.write( "     c) Find  center,  vertices, foci, <BR>\n" );
document.write( "         length of major and minor axes, <BR>\n" );
document.write( "        and eccentricity \r<BR>\n" );
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document.write( "d)	Sketch a graph of this ellipse.                     <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597200 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=597200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9x2 + 4y2 + 18x - 48y + 117 = 0 <BR>\n" );
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document.write( "9x^2 + 18x +   ;;;; +4y^2  - 48 y  =-117;; complete first square: 9(x^2+2x+1);; second 4(y^2-12y+36)\r<BR>\n" );
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document.write( " 9(x^2+2x+1)+ 4(y^2-12y+36)=-117 + 9 +144  ;;remember to multiply the coefficient by the constant that was factored out\r<BR>\n" );
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document.write( "9(x^2+2x+1)+ 4(y^2-12y+36)=36   ;;must divide both sides by 36 to make the right side 1.\r<BR>\n" );
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document.write( "(x+1)^2/4  + (y-6)^2/9=1<BR>\n" );
document.write( "Center is at (-1,6)<BR>\n" );
document.write( "Major axis is along y-axis. And it is a^2=9; a=3  Vertices are at (-1,3) and (-1,9)<BR>\n" );
document.write( "Minor axis is along x-axis.  And it is b^2-4; b=2  These are at (1,6) and (-3,6)<BR>\n" );
document.write( "Foci are a^2-c^2=b^2  They are at sqrt (5) from center. (-1, 6+ sqrt (5)) and (-1, 6-sqrt (5))<BR>\n" );
document.write( "Eccentricity is c/a which is sqrt(5)/3 </SPAN>\n" );
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