document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=746555>Question 746555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the center, vertices, and foci for the following ellipse 18x^2+4y^2-108x+16y=106\r<BR>\n" );
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document.write( "Write word or phrase that best completes each statement or answers question </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454396 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=454396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x%5E2%2B4y%5E2-108x%2B16y=106+ ALIGN=MIDDLE  ALT=\"18x%5E2%2B4y%5E2-108x%2B16y=106+\"   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=%2818x%5E2-108x%2B__%29%2B%284y%5E2%2B16y%2B___%29-106+=0 ALIGN=MIDDLE  ALT=\"%2818x%5E2-108x%2B__%29%2B%284y%5E2%2B16y%2B___%29-106+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....complete the square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818x%5E2-108x%2B162%29-162%2B%284y%5E2%2B32y%2B16%29-16-106=0 ALIGN=MIDDLE  ALT=\"%2818x%5E2-108x%2B162%29-162%2B%284y%5E2%2B32y%2B16%29-16-106=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=%2818x%5E2-108x%2B162%29%2B%284y%5E2%2B32y%2B16%29-284=0 ALIGN=MIDDLE  ALT=\"%2818x%5E2-108x%2B162%29%2B%284y%5E2%2B32y%2B16%29-284=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > from first group 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;\" > from second group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%28x%5E2-6x%2B9%29%2B4%28y%5E2%2B8y%2B4%29-284=0 ALIGN=MIDDLE  ALT=\"18%28x%5E2-6x%2B9%29%2B4%28y%5E2%2B8y%2B4%29-284=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=18%28x-3%29%5E2%2B4%28y%2B2%29%5E2=284 ALIGN=MIDDLE  ALT=\"18%28x-3%29%5E2%2B4%28y%2B2%29%5E2=284\"   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=18%28x-3%29%5E2%2F284%2B4%28y%2B2%29%5E2%2F284=284%2F284 ALIGN=MIDDLE  ALT=\"18%28x-3%29%5E2%2F284%2B4%28y%2B2%29%5E2%2F284=284%2F284\"   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-3%29%5E2%2F15.78%2B%28y%2B2%29%5E2%2F71=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F15.78%2B%28y%2B2%29%5E2%2F71=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...round <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.78 ALIGN=MIDDLE  ALT=\"15.78\"   DISABLED_style= \"max-width:90%; height:auto;\" > to whole number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2F16%2B%28y%2B2%29%5E2%2F71=1 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2F16%2B%28y%2B2%29%5E2%2F71=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the center is at: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " vertices: since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > term has the larger denominator, the ellipse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical ALIGN=MIDDLE  ALT=\"vertical\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "vertices (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B-sqrt%2871%29 ALIGN=MIDDLE  ALT=\"-2%2B-sqrt%2871%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8773; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6.43 ALIGN=MIDDLE  ALT=\"-6.43\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+10.43 ALIGN=MIDDLE  ALT=\"-+10.43\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
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document.write( "and foci:<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B-sqrt%28497%29%2F3 ALIGN=MIDDLE  ALT=\"-2%2B-sqrt%28497%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8773; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2B-7.43 ALIGN=MIDDLE  ALT=\"-2%2B-7.43\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8773;\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5.43 ALIGN=MIDDLE  ALT=\"-5.43\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+9.43 ALIGN=MIDDLE  ALT=\"-+9.43\"   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=drawing%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2Ccircle%283%2C-2%2C0.2%29%2C+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+-sqrt%28-4.5%28x-3%29%5E2%2B71%29-2%2Csqrt%28-4.5%28x-3%29%5E2%2B71%29-2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    </SPAN>\n" );
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