document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142383>Question 1142383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that y = −3/x and xy + 9 = 0 are equations that define two different hyperbolas. The line defined by x+y = 0 cuts each of the hyperbolas twice, at the points A and B (for y = −3/x) and C and D (for xy + 9 = 0). A and C are in the same quadrant; B and D are both in the quadrant opposite A and C.\r<BR>\n" );
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document.write( "Which of the following statements is/are true?\r<BR>\n" );
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document.write( "A. The hyperbolas have no points of intersection.<BR>\n" );
document.write( "B. The hyperbolas both lie in quadrants 2 and 4.<BR>\n" );
document.write( "C. The ratio of the x  -  coordinate of A to the x  -  coordinate of C is sqrt3/3.\r<BR>\n" );
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document.write( "1. Only A <BR>\n" );
document.write( "2. Only B <BR>\n" );
document.write( "3. Only C<BR>\n" );
document.write( "4. Only A and B <BR>\n" );
document.write( "5. A, B and C<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763107 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The equations are equivalent to y = -3/x and y = -9/x.<br><BR>\n" );
document.write( "Statement A: To see if there are any points of intersection, see what happens when you try to solve the pair of equations simultaneously.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Fx+=+-9%2Fx ALIGN=MIDDLE  ALT=\"-3%2Fx+=+-9%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  ???<br><BR>\n" );
document.write( "Statement B: If this is true, then x negative makes y positive (quadrant 2) and x positive makes y negative (quadrant 4).  Do these equations have that property?<br><BR>\n" );
document.write( "Statement C: To see if this is true, choose a simple value for x (1 is nearly always a good choice) and see what the resulting y values are. </SPAN>\n" );
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