document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=717075>Question 717075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how can I solve this use the eccentricity of each hyperbola to find its equation in standard form center(4,1),horizontal transverse axis is 12 and eccentricity 4/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440075 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=440075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of a hyperbola with a horizontal transverse axis can be written in the form<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;\" ><BR>\n" );
document.write( "I had to look it up (not good with names), but that is what is called the standard form.<BR>\n" );
document.write( "(h,k) is the center<BR>\n" );
document.write( "Center, vertices, and foci are on the horizontal line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=k ALIGN=MIDDLE  ALT=\"y=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the vertices,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2=a%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-h%29=a ALIGN=MIDDLE  ALT=\"abs%28x-h%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They are at distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the center, on line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=k ALIGN=MIDDLE  ALT=\"y=k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a ALIGN=MIDDLE  ALT=\"2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance between the vertices.<BR>\n" );
document.write( "The segment (and the distance) between the vertices is called the transverse axis.<BR>\n" );
document.write( " <BR>\n" );
document.write( "So far we know<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4 ALIGN=MIDDLE  ALT=\"h=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=1 ALIGN=MIDDLE  ALT=\"k=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=12 ALIGN=MIDDLE  ALT=\"2a=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The eccentricity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" > is defined based of the focal distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(distance from each focus to the center) as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=c%2Fa ALIGN=MIDDLE  ALT=\"e=c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and it turns out that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > are related by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=4%2F3 ALIGN=MIDDLE  ALT=\"e=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3=c%2F6 ALIGN=MIDDLE  ALT=\"4%2F3=c%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6%2A4%2F3 ALIGN=MIDDLE  ALT=\"c=6%2A4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=8 ALIGN=MIDDLE  ALT=\"c=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, plugging that (along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"c%5E2=a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%5E2=6%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"8%5E2=6%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64=36%2Bb%5E2 ALIGN=MIDDLE  ALT=\"64=36%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=64-36 ALIGN=MIDDLE  ALT=\"b%5E2=64-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=28 ALIGN=MIDDLE  ALT=\"b%5E2=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Finally, plugging the values given (or very easily found) for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   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;\" >, plus the hard earned value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the standard form we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-4%29%5E2%2F36-%28y-1%29%5E2%2F28=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-4%29%5E2%2F36-%28y-1%29%5E2%2F28=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );