document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194738>Question 1194738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the hyperbola with a center at (4, -1), transverse axis is parallel to the y-axis, distance between the foci is 10, one endpoint of the conjugate axis is at (6, -1).\r<BR>\n" );
document.write( "\n" );
document.write( "Answering this question would mean a lot to me, thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826992 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=826992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\r<BR>\n" );
document.write( "\n" );
document.write( " a center at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <BR>\n" );
document.write( "transverse axis is parallel to the y-axis, <BR>\n" );
document.write( "distance between the foci is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "one endpoint of the conjugate axis is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1 ALIGN=MIDDLE  ALT=\"+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " if the transverse axis is parallel to the y-axis, use the standard form\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if a center at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4 ALIGN=MIDDLE  ALT=\"h=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1 ALIGN=MIDDLE  ALT=\"k=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the distance from the center to the given endpoint of the conjugate axis, and we know  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4+ ALIGN=MIDDLE  ALT=\"a=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so far equation is\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-%28-1%29%29%5E2%2F4%5E2-%28x-4%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-%28-1%29%29%5E2%2F4%5E2-%28x-4%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2%2F16-%28x-4%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2%2F16-%28x-4%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The center is its midpoint, so the two foci are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is distance between center and foci, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c=5 ALIGN=MIDDLE  ALT=\"+c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The two blue lines are the latus rectums. They are given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2 ALIGN=MIDDLE  ALT=\"9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so by subtraction of half that or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F4 ALIGN=MIDDLE  ALT=\"9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the x-coordinate of the focus (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we get that<BR>\n" );
document.write( "the left end of the upper latus rectum is the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F4 ALIGN=MIDDLE  ALT=\"7%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%29.++The+hyperbola+goes+through+that+point.%0D%0A%0D%0A%7B%7B%7Bb%5E2=c%5E2-b%5E2=25-16=9 ALIGN=MIDDLE  ALT=\"4%29.++The+hyperbola+goes+through+that+point.%0D%0A%0D%0A%7B%7B%7Bb%5E2=c%5E2-b%5E2=25-16=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B1%29%5E2%2F16-%28x-4%29%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"%28y%2B1%29%5E2%2F16-%28x-4%29%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%284%2C-1%2C.12%29%2C+locate%284%2C-1%2CC%284%2C-1%29%29%2Ccircle%286%2C-1%2C.12%29%2C+locate%286%2C-1%2Cp%286%2C-1%29%29%2C%0D%0Acircle%284%2C4%2C.12%29%2C+locate%284%2C4%2CF%284%2C4%29%29%2C+circle%284%2C-6%2C.12%29%2C+locate%284%2C-6%2CF%284%2C-6%29%29%2C%0D%0Agreen%28line%284%2C4%2C4%2C-6%29%29%2Cblue%28line%287%2F4%2C4%2C25%2F4%2C4%29%2Cline%287%2F4%2C-6%2C25%2F4%2C-6%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F3%29%28-4sqrt%28x%5E2-8x%2B25%29+-+3%29%2C+%281%2F3%29%284sqrt%28x%5E2-8x%2B25%29+-+3%29%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );