document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039199>Question 1039199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hyperbola has a vertical transverse axis of length 14 and asymptotes of <BR>\n" );
document.write( "y=9/8x + 1 and y= -9/8x - 9. Find the center of the hyperbola, its focal length, and its eccentricity. \r<BR>\n" );
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document.write( "Can you please show me the work to get the center mainly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653970 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=653970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The center is the intersection of the asymptotes.<BR>\n" );
document.write( "That is the point that is a solution to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2Cy=-%289%2F8%29x-9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2Cy=-%289%2F8%29x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "You can solve that system of equations by substitution.<BR>\n" );
document.write( "For example, you could start by substituting the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F8%29x%2B1 ALIGN=MIDDLE  ALT=\"%289%2F8%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%289%2F8%29x-9 ALIGN=MIDDLE  ALT=\"y=-%289%2F8%29x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2Cy=-%289%2F8%29x-9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2Cy=-%289%2F8%29x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2C%289%2F8%29x%2B1=-%289%2F8%29x-9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2C%289%2F8%29x%2B1=-%289%2F8%29x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2C%289%2F8%29x%2B%289%2F8%29x=-9-1%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2C%289%2F8%29x%2B%289%2F8%29x=-9-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2C%289%2F4%29x=-10%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2C%289%2F4%29x=-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2Cx=-10%284%2F9%29%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2Cx=-10%284%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2Cx=-40%2F9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2Cx=-40%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and then, you could substitute the value found for one variable into one of the equations, to find the value of the other variable:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29x%2B1%2Cx=-40%2F9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29x%2B1%2Cx=-40%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29%28-40%2F9%29%2B1%2Cx=-40%2F9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29%28-40%2F9%29%2B1%2Cx=-40%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=%289%2F8%29%28-40%2F9%29%2B1%2Cx=-40%2F9%29 ALIGN=MIDDLE  ALT=\"system%28y=%289%2F8%29%28-40%2F9%29%2B1%2Cx=-40%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=-5%2B1%2Cx=-40%2F9%29 ALIGN=MIDDLE  ALT=\"system%28y=-5%2B1%2Cx=-40%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28y=-4%2Cx=-40%2F9%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28y=-4%2Cx=-40%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The asymptotes slopes give you the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fa=9%2F8 ALIGN=MIDDLE  ALT=\"b%2Fa=9%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ratio of conjugate to transverse axes.<BR>\n" );
document.write( "The transverse axis is the segment joining the vertices of the hyperbola.<BR>\n" );
document.write( "If the length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the distance from the center to each vertex must be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=14%2F2=7 ALIGN=MIDDLE  ALT=\"a=14%2F2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "From there you can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%28b%5E2%2Ba%5E2%29 ALIGN=MIDDLE  ALT=\"c=sqrt%28b%5E2%2Ba%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the eccentricity: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa ALIGN=MIDDLE  ALT=\"c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );