document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=695437>Question 695437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation foe a hyperbola with verticies at (0,3) and (-6,3) and asymptotes of y=x-6 and y= -x  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428553 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=428553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Something is wrong.<BR>\n" );
document.write( "The midpoint between your vertices is (-3,3).<BR>\n" );
document.write( "(Its coordinates are the averages of the coordinates of the vertices: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B%28-6%29%29%2F2=3%29 ALIGN=MIDDLE  ALT=\"%280%2B%28-6%29%29%2F2=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B3%29%2F2=3 ALIGN=MIDDLE  ALT=\"%283%2B3%29%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "That should be the center of the hyperbola, and the point where the asymptotes intersect.<BR>\n" );
document.write( "However, you asymptotes intersect at (3,-3).<BR>\n" );
document.write( " <BR>\n" );
document.write( "A hyperbola with axes parallel to the x-axis and y-axis would have an equation<BR>\n" );
document.write( "with a difference of squares involving x, y, and the coordinates of the center (h,k) of the hyperbola.<BR>\n" );
document.write( "The equation for a hyperbola with a horizontal transverse axis, opening left and right, like ) (, would look like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with asymptotes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28b%2Fa%29%28x-h%29+%2Bk ALIGN=MIDDLE  ALT=\"y=%28b%2Fa%29%28x-h%29+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-+%28b%2Fa%29%28x-h%29+%2Bk ALIGN=MIDDLE  ALT=\"y=+-+%28b%2Fa%29%28x-h%29+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > and vertices (h+a, k) and (h-a, k)<BR>\n" );
document.write( " <BR>\n" );
document.write( "The equation for a hyperbola with a vertical transverse axis, would look like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with asymptotes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28a%2Fb%29%28x-h%29+%2Bk ALIGN=MIDDLE  ALT=\"y=%28a%2Fb%29%28x-h%29+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-+%28a%2Fb%29%28x-h%29+%2Bk ALIGN=MIDDLE  ALT=\"y=+-+%28a%2Fb%29%28x-h%29+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > and vertices (h, a-k) and (h, a+k)\r<BR>\n" );
document.write( "\n" );
document.write( "If your asymptotes are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x ALIGN=MIDDLE  ALT=\"y=-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-6 ALIGN=MIDDLE  ALT=\"y=x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with slopes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b ALIGN=MIDDLE  ALT=\"a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You should be able to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b ALIGN=MIDDLE  ALT=\"a=b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the coordinates of the vertices.<BR>\n" );
document.write( "If your vertices are truly (0,3) and (-6,3), the center is (-3,3),<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the distance from the center to each of the vertices. </SPAN>\n" );
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