document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013652>Question 1013652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find the equation of the asymptote of 3x^2-2y^2=6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629915 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'm working from this reference:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/hyperbola.htm\" target = \"_blank\">http://www.purplemath.com/modules/hyperbola.htm</a>\r<BR>\n" );
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document.write( "this is the equation of a hyperbola.\r<BR>\n" );
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document.write( "the general form of the equation of a hyperbola is:\r<BR>\n" );
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document.write( "(x-h)^2 / a^2 - (y-k)^2 / b^2 = 1\r<BR>\n" );
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document.write( "your equation is 3x^2 - 2y^2 = 6\r<BR>\n" );
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document.write( "divide both sides of this equation by 6 to get:\r<BR>\n" );
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document.write( "3x^2/6 - 2y^2/6 = 1\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "x^2/2 - y^2/3 = 1\r<BR>\n" );
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document.write( "this means that a^2 = 2 and b^2 = 3\r<BR>\n" );
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document.write( "this means that a = sqrt(2) and b = sqrt(3)\r<BR>\n" );
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document.write( "the equation for the asymptotes of a horizontally aligned hyperbola is:\r<BR>\n" );
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document.write( "y = plus or minus (b/a)*(x-h) + k\r<BR>\n" );
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document.write( "since h and k are equal to 0, this equation becomes y = plus or minus (b/a)x.\r<BR>\n" );
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document.write( "since b = sqrt(3) and a = sqrt(2), this becomes y = plus or minus sqrt(3)/sqrt(2) * x.\r<BR>\n" );
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document.write( "since sqrt(3) / sqrt(2) is the same as sqrt(3/2), this becomes y = plus or minus sqrt(3/2) * x.\r<BR>\n" );
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document.write( "the equation of the asymptotes is y = plus or minus sqrt(3/2)x.\r<BR>\n" );
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document.write( "the following graph shows the equation of the hyperbola and the equations of the asymptotes.\r<BR>\n" );
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document.write( "all 6 of the blue equations point to the same hyperbola on the graph.<BR>\n" );
document.write( "those equations are equivalent to each other.<BR>\n" );
document.write( "the last 2 of the 6 go together.<BR>\n" );
document.write( "one of them is plus the square root of and the other is minus the square root of.\r<BR>\n" );
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document.write( "the red equations are the equations of the asymptotes of the hyperbola.<BR>\n" );
document.write( "one of them is plus the equation and the other is minus the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/011301.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "read the reference.<BR>\n" );
document.write( "there's lots of good information in there and it's not that hard to follow.\r<BR>\n" );
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