document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=812914>Question 812914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear sir/Ma'am,<BR>\n" );
document.write( "    Please help me with this math problem:<BR>\n" );
document.write( " center(1,-2), transverse axis parallel to the x-axis, transverse axis= 6, conjugate axis = 10. Find the equation of the hyperbola.<BR>\n" );
document.write( " Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #489403 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=489403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard forms for equations of ellipses are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for horizontally-oriented hyperbolas and<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;\" > for vertically-oriented hyperbolas<BR>\n" );
document.write( "Since the transverse axis is parallel to the x-axis in this problem, this hyperbola is horizontally-oriented. So we will be using the first form.<br><BR>\n" );
document.write( "In both forms, the coordinates of the center are represented by the 'h' and the 'k'. So with a center of (1, -2) out 'h' is 1 and our 'k' is -2.<br><BR>\n" );
document.write( "In both forms the 'a' represents the distance from the center to a vertex on the transverse axis. Since the center is halfway between the two vertices on the transverse axis, 'a' is 1/2 of the length of the transverse axis. This makes our 'a' 1/2 of 6 or, more simply, 3.<br><BR>\n" );
document.write( "With similar logic the 'b' is 1/2 the length of the conjugate axis. So our 'b' is 1/2 of 10 or just 5.<br><BR>\n" );
document.write( "With our 'h', 'k', 'a' and 'b' we are now ready to write the equation. Inserting the values we have found into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%281%29%29%5E2%2F%283%29%5E2+-+%28y-%28-2%29%29%5E2%2F%285%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-%281%29%29%5E2%2F%283%29%5E2+-+%28y-%28-2%29%29%5E2%2F%285%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2F9+-+%28y%2B2%29%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2F9+-+%28y%2B2%29%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );