document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=770449>Question 770449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the hyperbola whose centre is (1, 0), one focus is (6, 0) and transverse axis 6.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #469546 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=469546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With the center at (1,0) and a focus 5 units to the right, at (6,0), you know that the focal distance is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=5 ALIGN=MIDDLE  ALT=\"c=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > anf that the transverse axis is along the x-axis.<BR>\n" );
document.write( "(You also know that the other focus will be 5 units to the left of the center, at (4,0), and that is useful if you need to sketch the hyperbola).<BR>\n" );
document.write( "The equation of a hyperbola with a transverse axis parallel to the x-axis and center at (h,k) is<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( "In this case, since the center is (1,0), the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance from a vertex to the center, half of the length of the transverse axis.<BR>\n" );
document.write( "If the transverse axis is 6, the vertices are 6 units apart,<BR>\n" );
document.write( "and they are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6%2F2=3 ALIGN=MIDDLE  ALT=\"a=6%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units from the center.<BR>\n" );
document.write( "(If you need to sketch the hyperbola, the vertices are 3 units to the right and 3 units to the left of the center, at (-2,0) and (4,0)).<BR>\n" );
document.write( "The other number you need for the equation of the hyperbola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that<BR>\n" );
document.write( "<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( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2=3%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"5%5E2=3%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=9%2Bb%5E2 ALIGN=MIDDLE  ALT=\"25=9%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=25-9 ALIGN=MIDDLE  ALT=\"b%5E2=25-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=16 ALIGN=MIDDLE  ALT=\"b%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the equation of the hyperbola in question is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-1%29%5E2%2F3%5E2-y%5E2%2F4%5E2=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-1%29%5E2%2F3%5E2-y%5E2%2F4%5E2=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-1%29%5E2%2F9-y%5E2%2F16=1%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-1%29%5E2%2F9-y%5E2%2F16=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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