document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199546>Question 1199546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the hyperbola xy = 1. Determine the new equation of this hyperbola if the x,y axes are rotated about the origin by 45 degrees clockwise. <BR>\n" );
document.write( "Answer: y^2 - x^2 = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833481 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The transformation for a clockwise rotation through an angle A<BR>\n" );
document.write( "about the origin is:<BR>\n" );
document.write( "x' = xcos(A) + ysin(A)<BR>\n" );
document.write( "y' = -xsin(A) + ycos(A)<BR>\n" );
document.write( "In this case, A = 45 deg, so the transformed coordinates are:<BR>\n" );
document.write( "x' = x/sqrt(2) + y/sqrt(2)<BR>\n" );
document.write( "y' = -x/sqrt(2) + y/sqrt(2)<BR>\n" );
document.write( "x'*y' = -x^2/2 + y^2/2 = 1 -> y^2 - x^2 = 2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );