document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121763>Question 1121763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to find a b and c, eccentricity, directrix, sf, gf endpoints of LR, LR B, V(vertex) and foci<BR>\n" );
document.write( "9x^2 + 4y^2 - 24y -72 + 144 = 0 <BR>\n" );
document.write( "(ellipse) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737777 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+%2B+4y%5E2+-+24y+-72++%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9x%5E2+%2B+4y%5E2+-+24y+-72++%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...-> I guess you got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x ALIGN=MIDDLE  ALT=\"72x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2+%2B+4y%5E2+-+24y+-72x+%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9x%5E2+%2B+4y%5E2+-+24y+-72x+%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%5E2-72x+%29%2B+%284y%5E2+-+24y+%29+%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"%289x%5E2-72x+%29%2B+%284y%5E2+-+24y+%29+%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x%5E2-8x+%29%2B4+%28y%5E2+-+6y+%29+%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9%28x%5E2-8x+%29%2B4+%28y%5E2+-+6y+%29+%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x%5E2-8x%2Bb%5E2+%29+-9b%5E2%2B4+%28y%5E2+-+6y+%2Bb%5E2%29+-4b%5E2%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9%28x%5E2-8x%2Bb%5E2+%29+-9b%5E2%2B4+%28y%5E2+-+6y+%2Bb%5E2%29+-4b%5E2%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x%5E2-8x%2B4%5E2+%29+-9%2A4%5E2%2B4+%28y%5E2+-+6y+%2B3%5E2%29+-4%2A3%5E2%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9%28x%5E2-8x%2B4%5E2+%29+-9%2A4%5E2%2B4+%28y%5E2+-+6y+%2B3%5E2%29+-4%2A3%5E2%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-4%29%5E2++-9%2A16%2B4+%28y+-+3%29%5E2+-4%2A9%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9%28x-4%29%5E2++-9%2A16%2B4+%28y+-+3%29%5E2+-4%2A9%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-4%29%5E2++-144%2B4+%28y+-+3%29%5E2+-36%2B+144+=+0+ ALIGN=MIDDLE  ALT=\"9%28x-4%29%5E2++-144%2B4+%28y+-+3%29%5E2+-36%2B+144+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-4%29%5E2+%2B4+%28y+-+3%29%5E2+-36+=+0+ ALIGN=MIDDLE  ALT=\"9%28x-4%29%5E2+%2B4+%28y+-+3%29%5E2+-36+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-4%29%5E2+%2B4+%28y+-+3%29%5E2+=+36+ ALIGN=MIDDLE  ALT=\"9%28x-4%29%5E2+%2B4+%28y+-+3%29%5E2+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x-4%29%5E2%2F+36+%2B4+%28y+-+3%29%5E2+%2F36+=+36+%2F36+ ALIGN=MIDDLE  ALT=\"9%28x-4%29%5E2%2F+36+%2B4+%28y+-+3%29%5E2+%2F36+=+36+%2F36+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2F+4+%2B%28y+-+3%29%5E2+%2F9=1 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2F+4+%2B%28y+-+3%29%5E2+%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "major axis is vertical, so compare to  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%2Fa%5E2+=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%2Fa%5E2+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you see that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4 ALIGN=MIDDLE  ALT=\"h=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=4 ALIGN=MIDDLE  ALT=\"b%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=9 ALIGN=MIDDLE  ALT=\"a%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "eccentricity : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa ALIGN=MIDDLE  ALT=\"c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "first find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=3%5E2-2%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=3%5E2-2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=9-4 ALIGN=MIDDLE  ALT=\"c%5E2=9-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=5 ALIGN=MIDDLE  ALT=\"c%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%285%29 ALIGN=MIDDLE  ALT=\"c=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " eccentricity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8776; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.76 ALIGN=MIDDLE  ALT=\"0.76\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "center: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "foci : (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+-+sqrt%285%29 ALIGN=MIDDLE  ALT=\"3+-+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+sqrt%285%29 ALIGN=MIDDLE  ALT=\"3+%2B+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "or &#8776; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.76 ALIGN=MIDDLE  ALT=\"0.76\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  and  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.24 ALIGN=MIDDLE  ALT=\"5.24\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "vertices:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  and  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6 ALIGN=MIDDLE  ALT=\"+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "covertices: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  and  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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