document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204201>Question 1204201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation in standard form for the ellipse with center at (5, 8), horizontal axis of length 10 and passes through the point (6, 4). </SPAN>\n" );
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document.write( "We can't tell with the given information whether the horizontal axis is the major or minor axis.  We can assume it is the major axis and then adjust our results if it turns out that it is the minor axis.<br><BR>\n" );
document.write( "The standard form with center at (5,8) and horizontal major axis of length 10 is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2F5%5E2%2B%28y-8%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2F5%5E2%2B%28y-8%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Find b^2 using the given point (6,4) on the ellipse.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-5%29%5E2%2F5%5E2%2B%284-8%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%286-5%29%5E2%2F5%5E2%2B%284-8%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F25%2B16%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"1%2F25%2B16%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Fb%5E2=24%2F25 ALIGN=MIDDLE  ALT=\"16%2Fb%5E2=24%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24b%5E2=400 ALIGN=MIDDLE  ALT=\"24b%5E2=400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=400%2F24=50%2F3 ALIGN=MIDDLE  ALT=\"b%5E2=400%2F24=50%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Note that b^2=50/3 is less than a^2=25, so the horizontal axis is indeed the major axis.<br><BR>\n" );
document.write( "The standard form of the equation of the ellipse is<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2F25%2B%28y-8%29%5E2%2F%2850%2F3%29=1 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2F25%2B%28y-8%29%5E2%2F%2850%2F3%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );