document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195733>Question 195733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool.<BR>\n" );
document.write( "I'm not sure where to start?<BR>\n" );
document.write( "y^2=1-x^2/324 and then square both sides? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146778 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=146778\">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%2F324+%2B+y%5E2%2F196+=+1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F324+%2B+y%5E2%2F196+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F18%5E2+%2B+y%5E2%2F196+=+1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F18%5E2+%2B+y%5E2%2F196+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=324 ALIGN=MIDDLE  ALT=\"324\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%5E2 ALIGN=MIDDLE  ALT=\"18%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=x%5E2%2F18%5E2+%2B+y%5E2%2F14%5E2+=+1+ ALIGN=MIDDLE  ALT=\"x%5E2%2F18%5E2+%2B+y%5E2%2F14%5E2+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=196 ALIGN=MIDDLE  ALT=\"196\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%5E2 ALIGN=MIDDLE  ALT=\"14%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the equation is now in the form <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;\" > (which is the general equation of an ellipse) where <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=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=18 ALIGN=MIDDLE  ALT=\"a=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=14 ALIGN=MIDDLE  ALT=\"b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The longest distance between any two points along a line on the ellipse falls on the major axis. The length of the semi major axis simply turns out to be the larger value of \"a\" or \"b\"\r<BR>\n" );
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document.write( "Since \"a\" is larger, this means that the length of the semi major axis is 18 units. Double this value to get 36 units.\r<BR>\n" );
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document.write( "So the the longest distance across the pool is 36 units.\r<BR>\n" );
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document.write( "For the shortest distance, just use the smaller value 14 and double it to 28. \r<BR>\n" );
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document.write( "So the the shortest distance across the pool is 28 units. </SPAN>\n" );
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