document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169058>Question 1169058</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a point moves so that the difference between its distance from (3,0) and (-3,0) is 4. find the equation of its locus<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794159 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794159\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "This is the definition of a hyperbola with foci at (3,0) and (-3,0); that means the center is at (0,0), and the major axis is horizontal.  The general equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In that equation, a is the semi-major axis (distance from the center to each vertex) and b is the semi-minor axis.<br><BR>\n" );
document.write( "a and b are related by the equation<br><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><BR>\n" );
document.write( "where c is the distance from the center to each focus.<br><BR>\n" );
document.write( "In this example, then, we know c=3.<br><BR>\n" );
document.write( "It is easy to find the two points on the x-axis that are on the graph and are therefore the vertices.  With a distance of 6 between the two vertices, and a difference of 4 between the distances of a point from the two vertices, the vertices are at (2,0) and (-2,0); that makes a=2 and a^2=4.<br><BR>\n" );
document.write( "Then using <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;\" >, we find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=5 ALIGN=MIDDLE  ALT=\"b%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So the equation of the locus is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4-y%5E2%2F5=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4-y%5E2%2F5=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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