document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=459116>Question 459116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do I graph 25(x+2)^2-9(y-1)^2=225 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316258 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=316258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how do I graph 25(x+2)^2-9(y-1)^2=225<BR>\n" );
document.write( "..<BR>\n" );
document.write( "25(x+2)^2-9(y-1)^2=225<BR>\n" );
document.write( "divide by 225<BR>\n" );
document.write( "(x+2)^2/9-(y-1)^2/25=1<BR>\n" );
document.write( "This equation is a hyperbola with horizontal transverse axis. (Note the minus sign and the x-term comes before the y-term)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of (x-h) and (y-k)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "center(-2,1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3<BR>\n" );
document.write( "length of transverse axis=2a=6<BR>\n" );
document.write( "vertices=(-2±3,1)=(-5,1) and (1,1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=25<BR>\n" );
document.write( "b=5<BR>\n" );
document.write( "length of conjugate axis=2b=10<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes:<BR>\n" );
document.write( "slope, m=±b/a=±5/3<BR>\n" );
document.write( "Equations:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "1=5(-2)/3+b<BR>\n" );
document.write( "b=1+10/3=13/3<BR>\n" );
document.write( "y=5x/3+13/3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "1=-5(-2)/3+b<BR>\n" );
document.write( "b=1-10/3=-7/3<BR>\n" );
document.write( "y=-5x/3-7/3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=(-25+25(x+2)^2/9)^.5+1<BR>\n" );
document.write( "See graph below as a visual check on answers above:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%28-25%2B25%28x%2B2%29%5E2%2F9%29%5E.5%2B1%2C-%28-25%2B25%28x%2B2%29%5E2%2F9%29%5E.5%2B1%2C5x%2F3%2B13%2F3%2C-5x%2F3-7%2F3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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