document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147808>Question 147808</A>: <I><SPAN STYLE=\"word-break: break-all;\">  My question is: Write the equation for the ellipse whose center is the origin, has a horizontal major axis length of 12 and passses through the point (-4,2).<BR>\n" );
document.write( "I need help with this, since the horizontal axis is at the origin I get that the foci is (-6,0) and (6,0). I find that the equation will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > but I am having trouble finding what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals. Can you help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108203 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font size = 9 color = \"red\">SOLUTION BY EDWIN</font></b>\r<BR>\n" );
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document.write( " My question is: Write the equation for the ellipse whose center is the origin, has a horizontal major axis length of 12 and passses through the point (-4,2).<BR>\n" );
document.write( "I need help with this, since the horizontal axis is at the origin I get that the foci is (-6,0) and (6,0). I find that the equation will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > but I am having trouble finding what <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > equals. Can you help me?\r<BR>\n" );
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document.write( "Go back and look at the problem to see what if anything you haven't used. Here's what you haven't used:\r<BR>\n" );
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document.write( ">>...passses through the point (-4,2)...<<\r<BR>\n" );
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document.write( "So you see that all you need do is plug the point (-4,2) into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-4%29%5E2%2F36%29%2B%28%282%29%5E2%2Fb%5E2%29=1 ALIGN=MIDDLE  ALT=\"%28%28-4%29%5E2%2F36%29%2B%28%282%29%5E2%2Fb%5E2%29=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=16%2F36%2B4%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"16%2F36%2B4%2Fb%5E2=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=4%2F9%2B4%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"4%2F9%2B4%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Clear of fractions by multiplying thru by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9b%5E2 ALIGN=MIDDLE  ALT=\"9b%5E2\"   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=9b%5E2%2A4%2F9%2B9b%5E2%2A4%2Fb%5E2=9b%5E2%2A1 ALIGN=MIDDLE  ALT=\"9b%5E2%2A4%2F9%2B9b%5E2%2A4%2Fb%5E2=9b%5E2%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%289%29b%5E2%2A4%2Fcross%289%29%2B9cross%28b%5E2%29%2A4%2Fcross%28b%5E2%29=9b%5E2 ALIGN=MIDDLE  ALT=\"cross%289%29b%5E2%2A4%2Fcross%289%29%2B9cross%28b%5E2%29%2A4%2Fcross%28b%5E2%29=9b%5E2\"   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=4b%5E2%2B36=9b%5E2 ALIGN=MIDDLE  ALT=\"4b%5E2%2B36=9b%5E2\"   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=36=5b%5E2 ALIGN=MIDDLE  ALT=\"36=5b%5E2\"   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=36%2F5=b%5E2 ALIGN=MIDDLE  ALT=\"36%2F5=b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That's an ugly answer, but it is correct.  So<BR>\n" );
document.write( "the equation of the ellipse in standard form is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36%2By%5E2%2F%2836%2F5%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2By%5E2%2F%2836%2F5%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is its graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C+grid%281%29%2C+locate%28-4-.2%2C2.4%2C%22@%22%29%2C+graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28%2836-x%5E2%29%2F5%29%29%2C+locate%28-6.4-.2%2C2.7%2C%22%28-4%2C2%29%22%29%2C+%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-sqrt%28%2836-x%5E2%29%2F5%29%29%0D%0A+%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But if you don't necessarily have to have it in standard<BR>\n" );
document.write( "form, you can simplify it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F36%2By%5E2%2F%2836%2F5%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2By%5E2%2F%2836%2F5%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply top and bottom of the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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%2F36%2B5y%5E2%2F%285%2A%2836%2F5%29%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2B5y%5E2%2F%285%2A%2836%2F5%29%29=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%2F36%2B5y%5E2%2F%28cross%285%29%2A%2836%2Fcross%285%29%29%29=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2B5y%5E2%2F%28cross%285%29%2A%2836%2Fcross%285%29%29%29=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%2F36%2B5y%5E2%2F36=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F36%2B5y%5E2%2F36=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then multiply through by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"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=x%5E2%2B5y%5E2=36 ALIGN=MIDDLE  ALT=\"x%5E2%2B5y%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Edwin</pre></font></b>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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