document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065505>Question 1065505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The asymptotes of a hyperbola are y=2x and y=-2x.  If the hyperbola passes through the point (9, 16), find the x-intercepts of the hyperbola. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680703 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=680703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A hyperbola that has x-intercepts has an equation of the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and its asymptotes are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28b%2Fa%29%2Ax ALIGN=MIDDLE  ALT=\"y=%28b%2Fa%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28b%2Fa%29%2Ax ALIGN=MIDDLE  ALT=\"y=-%28b%2Fa%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so for this problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa=2 ALIGN=MIDDLE  ALT=\"b%2Fa=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2a ALIGN=MIDDLE  ALT=\"b=2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That makes the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2-y%5E2%2F4a%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2-y%5E2%2F4a%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so far.<BR>\n" );
document.write( "To find the value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=9%2Cy=16%29 ALIGN=MIDDLE  ALT=\"system%28x=9%2Cy=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the coordinates of point (9,16) .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"9%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22-%22 ALIGN=MIDDLE  ALT=\"%22-%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%5E2%2F4a%5E2=1 ALIGN=MIDDLE  ALT=\"16%5E2%2F4a%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81%2Fa%5E2 ALIGN=MIDDLE  ALT=\"81%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22-%22 ALIGN=MIDDLE  ALT=\"%22-%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256%2F4a%5E2=1 ALIGN=MIDDLE  ALT=\"256%2F4a%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying both sides of the equal sign times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E2 ALIGN=MIDDLE  ALT=\"4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A81-256=4a%5E2 ALIGN=MIDDLE  ALT=\"4%2A81-256=4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=324-256=4a%5E2 ALIGN=MIDDLE  ALT=\"324-256=4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68=4a%5E2 ALIGN=MIDDLE  ALT=\"68=4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=68%2F4=17 ALIGN=MIDDLE  ALT=\"a%5E2=68%2F4=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the equation we were looking for is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2F17-y%5E2%2F68=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2F17-y%5E2%2F68=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );