document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=373977>Question 373977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following is an equation of one of the asymptotes of the hyperbola:<BR>\n" );
document.write( "3x2-3y2=48? <BR>\n" );
document.write( "    x-y=0  <BR>\n" );
document.write( "   3x-3y=0  <BR>\n" );
document.write( "   y-3x=0  <BR>\n" );
document.write( "   x+27y=0  <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266177 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which of the following is an equation of one of the asymptotes of the hyperbola:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-3y%5E2=48 ALIGN=MIDDLE  ALT=\"3x%5E2-3y%5E2=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First we must get the equation in either the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Either way we get a 1 on the right side by dividing every term<BR>\n" );
document.write( "by 48.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2F48-3y%5E2%2F48=48%2F48 ALIGN=MIDDLE  ALT=\"3x%5E2%2F48-3y%5E2%2F48=48%2F48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F16-y%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F16-y%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Comparing to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we see that <BR>\n" );
document.write( "aČ=16 and bČ=16 and so a=4, b=4\r<BR>\n" );
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document.write( "The defining rectangle is then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C+%0D%0A%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%29%2C+green%28rectangle%28-4%2C-4%2C4%2C4%29%2Cline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%28-4%2C-4%2C4%2C-4%29%0D%0A%0D%0A%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So its extended diagonals are the asymptotes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C+%0D%0A%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-sqrt%28x%5E2-16%29%29%2C+green%28rectangle%28-4%2C-4%2C4%2C4%29%2Cline%28-4%2C4%2C4%2C4%29%2C%0D%0Aline%28-4%2C-4%2C4%2C-4%29%2C+line%28-11%2C-11%2C11%2C11%29%2Cline%28-11%2C11%2C11%2C-11%29%2C%0D%0A%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28x%5E2-16%29%29++%0D%0A%0D%0A%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And they have slope ±1 and pass through the origin so their equations are<BR>\n" );
document.write( "y = x  and y = -x\r<BR>\n" );
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document.write( "In standard form these are\r<BR>\n" );
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document.write( "x-y=0 and x+y=0\r<BR>\n" );
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document.write( "x-y=0 is one of the choices.  But I notice that there is also<BR>\n" );
document.write( "the choice 3x-3y=0, which is equivalent to x-y=0.  So either<BR>\n" );
document.write( "of these would technically be correct.\r<BR>\n" );
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document.write( "Edwin</pre> <BR>\n" );
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