document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996230>Question 996230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem:<BR>\n" );
document.write( "Identify the conic section whose equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+4y%5E2+-+16y+=+0 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+4y%5E2+-+16y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and write the equation in standard form.<BR>\n" );
document.write( "Describe as completely as possible the conic section.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614750 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=614750\">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=+x%5E2+%2B+4y%5E2+-+16y+=+0 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+4y%5E2+-+16y+=+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=+x%5E2+%2B+4%28y%5E2+-+4y+%29=+0 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+4%28y%5E2+-+4y+%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >........complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F4+%2B+%28y%5E2+-+4y%2B2%5E2%29-4=+0 ALIGN=MIDDLE  ALT=\"+x%5E2%2F4+%2B+%28y%5E2+-+4y%2B2%5E2%29-4=+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=+x%5E2%2F4+%2B+%28y-+2%29%5E2-4=+0 ALIGN=MIDDLE  ALT=\"+x%5E2%2F4+%2B+%28y-+2%29%5E2-4=+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=+x%5E2%2F4+%2B+%28y-+2%29%5E2=4 ALIGN=MIDDLE  ALT=\"+x%5E2%2F4+%2B+%28y-+2%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   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=+x%5E2%2F16+%2B+%28y-+2%29%5E2%2F4=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F16+%2B+%28y-+2%29%5E2%2F4=+1\"   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=+x%5E2%2F16+%2B%28y-+2%29%5E2%2F4=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F16+%2B%28y-+2%29%5E2%2F4=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F16 ALIGN=MIDDLE  ALT=\"+x%5E2%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can write as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-0%29%5E2%2F16 ALIGN=MIDDLE  ALT=\"+%28x-0%29%5E2%2F16\"   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-0%29%5E2%2F16+%2B%28y-+2%29%5E2%2F4=+1 ALIGN=MIDDLE  ALT=\"+%28x-0%29%5E2%2F16+%2B%28y-+2%29%5E2%2F4=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have an ellipse that has:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>semi-major axis length<BR>\n" );
document.write( "<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;\" >=>semi-minor axis length<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=4%5E2-2%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=4%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=12 ALIGN=MIDDLE  ALT=\"c%5E2=12\"   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%2812%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"c=2sqrt%283%29\"   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=0 ALIGN=MIDDLE  ALT=\"0\"   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;\" >)<BR>\n" );
document.write( "foci : (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-c ALIGN=MIDDLE  ALT=\"-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   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;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2sqrt%283%29 ALIGN=MIDDLE  ALT=\"-2sqrt%283%29\"   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;\" >)<BR>\n" );
document.write( "vertices:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >),  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-a ALIGN=MIDDLE  ALT=\"4-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " (<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=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<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=2 ALIGN=MIDDLE  ALT=\"2\"   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=2sqrt%283%29%2F4=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"c%2Fa=2sqrt%283%29%2F4=sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Csqrt%284%281-%28x-0%29%5E2%2F16%29+%29%2B2%2C-sqrt%284%281-%28x-0%29%5E2%2F16%29+%29%2B2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );