document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173642>Question 173642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the ellipse that satisfies the given conditions.\r<BR>\n" );
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document.write( "Vertices are (+-5,0), foci (+-sqrt(21),0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128592 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=128592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think the following graph is it.<BR>\n" );
document.write( "look below the graph for further comments.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-6%2C6%2C-6%2C6%2Csqrt%28%28100-4x%5E2%29%2F25%29%2C-sqrt%28%28100-4x%5E2%29%2F25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "standard equation of a ellipse where the major axis is horizontal and the center of the ellipse is at the origin is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Fa%5E2%29+%2B+%28y%5E2%2Fb%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Fa%5E2%29+%2B+%28y%5E2%2Fb%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "hard to explain but a decent treatment of this can be found at the following web address:<BR>\n" );
document.write( "http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_conics_ellipse.xml<BR>\n" );
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document.write( "you are given:<BR>\n" );
document.write( "vertices are: (+-5,0)<BR>\n" );
document.write( "focii are: (+-sqrt(21),0)<BR>\n" );
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document.write( "since the focii are on the x-axis, then this equation has a major axis as horizontal.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this make a = 5, since the a is the distance from the horizontal vertex to the origin.<BR>\n" );
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document.write( "we need to find b.<BR>\n" );
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document.write( "use the equation <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;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "c is the distance from the focus to the origin.<BR>\n" );
document.write( "that would be sqrt(21)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the equation is:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "substituting:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+=+25+-+b%5E2 ALIGN=MIDDLE  ALT=\"21+=+25+-+b%5E2\"   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+=+25-21+=+4 ALIGN=MIDDLE  ALT=\"b%5E2+=+25-21+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 2<BR>\n" );
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document.write( "we have:<BR>\n" );
document.write( "a = 5<BR>\n" );
document.write( "b = 2<BR>\n" );
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document.write( "standard equation becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F25+%2B+y%5E2%2F4+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F25+%2B+y%5E2%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to graph this solve for y:<BR>\n" );
document.write( "that equation becomes:<BR>\n" );
document.write( "y = +/- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28100-4x%5E2%29%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28100-4x%5E2%29%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "sorry for the rush job but i ran out of time.<BR>\n" );
document.write( "hopefully this helps.<BR>\n" );
document.write( "check that website out.<BR>\n" );
document.write( "decent treatment of the subject.<BR>\n" );
document.write( " </SPAN>\n" );
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