document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=743731>Question 743731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the hyperbola that the transverse axis is parallel to the x-axis, center at (2,-2), passing through (2+3&#8730;2,0) and (2+3&#8730;10,4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453037 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the hyperbola that the transverse axis is parallel to the x-axis, center at (2,-2), passing through (2+3&#8730;2,0) and (2+3&#8730;10,4).<BR>\n" );
document.write( "***<BR>\n" );
document.write( "This is a hyperbola with horizontal transverse axis.<BR>\n" );
document.write( "Its standard form of equation: <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;\" >, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "Given center: (2,-2)<BR>\n" );
document.write( "Equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2Fa%5E2-%28y%2B2%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2Fa%5E2-%28y%2B2%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using given coordinates to solve for a and b:<BR>\n" );
document.write( "(2+3&#8730;2-2)^2/a^2-(0+2)^2/b^2=1<BR>\n" );
document.write( "(2+3&#8730;10-2)^2/a^2-(4+2)^2/b^2=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "18/a^2-4/b^2=1<BR>\n" );
document.write( "90/a^2-36/b^2=1<BR>\n" );
document.write( "let x=1/a^2<BR>\n" );
document.write( "let y=1/b^2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "18x-4y=1<BR>\n" );
document.write( "90x-36y=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "-162x+36y=-9<BR>\n" );
document.write( "90x-36y=1<BR>\n" );
document.write( "add<BR>\n" );
document.write( "-72x=-8<BR>\n" );
document.write( "x=8/72=1/9=1/a^2<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "..<BR>\n" );
document.write( "4y=18x-1=2-1=1<BR>\n" );
document.write( "y=1/4=1/b^2<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "Equation of given hyperbola:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2F9-%28y%2B2%29%5E2%2F4=1 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2F9-%28y%2B2%29%5E2%2F4=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );