document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120791>Question 1120791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rotate the axes to eliminate the xy-term in the equation.Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes.\r<BR>\n" );
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document.write( "b. xy – 2y – 4x = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736780 by </B><A HREF=/tutors/aboutme.mpl?userid=Alex.33><B>Alex.33(110)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alex.33><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=Alex.33><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To rotate axes by a radians (note that a is confined within (0, pi))(Personally I'd like to do it counterclockwise, but you're free to do otherwise), you'll need to convert the coordinates accordingly, which can be proved with a little simple geometry.\r<BR>\n" );
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document.write( "x=x'cosa-y'sina<BR>\n" );
document.write( "y=x'sina+y'cosa\r<BR>\n" );
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document.write( "Put them into the equation you gave:<BR>\n" );
document.write( "sina*cosa*(x'^2-y'^2)+((cosa)^2-(sina)^2)x'y'-2(x'sina+y'cosa)-4(x'cosa-y'sina)=0<BR>\n" );
document.write( "Aha! To succeed, we just need to get the coefficient of the term x'y' equal to 0.\r<BR>\n" );
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document.write( "(cosa)^2-(sina)^2=cos(2a)=0.<BR>\n" );
document.write( "a=pi/4 or 3pi/4.\r<BR>\n" );
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document.write( "And it's done.<BR>\n" );
document.write( "//SORRY FOR THE ERROR WITH THE FOMULA GENERATOR. \r<BR>\n" );
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document.write( "Wanna know more? check this out http://www.sparknotes.com/math/precalc/conicsections/section5/#_motz_ </SPAN>\n" );
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