document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204200>Question 1204200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the ellipse that has a center at (5,-4), a vertex at (12,-4), and a covertex at (5,-6). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840315 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=840315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard form of the equation of an ellipse with center <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h ALIGN=MIDDLE  ALT=\"+h\"   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;\" >) and major axis parallel to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x ALIGN=MIDDLE  ALT=\"+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-axis is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"+%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a%3Eb ALIGN=MIDDLE  ALT=\"+a%3Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the length of the major axis is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a ALIGN=MIDDLE  ALT=\"+2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the coordinates of the vertices are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++h+ ALIGN=MIDDLE  ALT=\"++h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >±<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;\" >)<BR>\n" );
document.write( "the length of the minor axis is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++2b ALIGN=MIDDLE  ALT=\"++2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the coordinates of the co-vertices are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++h ALIGN=MIDDLE  ALT=\"++h\"   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=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "the coordinates of the foci are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++h ALIGN=MIDDLE  ALT=\"++h\"   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;\" >), where <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;\" >\r<BR>\n" );
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document.write( "the ellipse that has \r<BR>\n" );
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document.write( "a center at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4 ALIGN=MIDDLE  ALT=\"+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( " <BR>\n" );
document.write( "Thus, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=5 ALIGN=MIDDLE  ALT=\"+h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k=-4 ALIGN=MIDDLE  ALT=\"+k=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vertex at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+12 ALIGN=MIDDLE  ALT=\"+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ± <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=+-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=+5%2Ba=12 ALIGN=MIDDLE  ALT=\"+5%2Ba=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a=12-5 ALIGN=MIDDLE  ALT=\"+a=12-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a=7 ALIGN=MIDDLE  ALT=\"+a=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a covertex at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   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;\" >)=>(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<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=+b ALIGN=MIDDLE  ALT=\"+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4%2Bb=-6 ALIGN=MIDDLE  ALT=\"+-4%2Bb=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=6-4 ALIGN=MIDDLE  ALT=\"+b=6-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" >\r<BR>\n" );
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document.write( "your ellipse is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-5%29%5E2%2F7%5E2%2B%28y-%28-4%29%29%5E2%2F2%5E2=1 ALIGN=MIDDLE  ALT=\"+%28x-5%29%5E2%2F7%5E2%2B%28y-%28-4%29%29%5E2%2F2%5E2=1\"   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=+%28x-5%29%5E2%2F49%2B%28y%2B4%29%5E2%2F4=1 ALIGN=MIDDLE  ALT=\"+%28x-5%29%5E2%2F49%2B%28y%2B4%29%5E2%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<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+-10%2C+15%2C+-10%2C+10%2C%0D%0Acircle%285%2C-4%2C.12%29%2C+locate%285%2C-4%2CC%285%2C-4%29%29%2C%0D%0Acircle%2812%2C-4%2C.12%29%2C+locate%2812%2C-4%2CV%2812%2C-4%29%29%2C%0D%0Acircle%285%2C-6%2C.12%29%2C+locate%285%2C-6%2Cco-V%285%2C-6%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+15%2C+-10%2C+10%2C+%282%2F7%29%28-sqrt%28-x%5E2%2B10x%2B24%29-14%29%2C+%282%2F7%29%28sqrt%28-x%5E2%2B10x%2B24%29-14%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );