document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=435851>Question 435851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is 36x^2-9y^2=324 in standard form? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302143 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=302143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what is 36x^2-9y^2=324 in standard form?<BR>\n" );
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document.write( "36x^2-9y^2=324<BR>\n" );
document.write( "x^2/9-y^2/36=1<BR>\n" );
document.write( "This is a hyperbola with standard form, (x-h)^2/a^2-(y-k)^2/b^2=1<BR>\n" );
document.write( "(Note: If the minus sign were a plus sign, the equation would be an ellipse.)<BR>\n" );
document.write( "In this case, (h,k)=(0,0), so the center is at the origin ((),0).<BR>\n" );
document.write( "Since x^2 comes before y^2, it has a horizontal transverse axis.<BR>\n" );
document.write( "If y^2 came before x^2, it would have had a vertical transverse axis.<BR>\n" );
document.write( "a^2=9<BR>\n" );
document.write( "a=3=(distance from center to vertices<BR>\n" );
document.write( "b^2=36<BR>\n" );
document.write( "b=6<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "c=sqrt(a^2+b^2)=sqrt(45)=6.7=distance from center to foci.<BR>\n" );
document.write( "asymptotes go thru center and have slopes of +and -b/a=+-2<BR>\n" );
document.write( "equation of asymptotes: y=+-2x<BR>\n" );
document.write( "See graph of hyperbola below:\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "y=+-(36(x^2/9-1))^.5\r<BR>\n" );
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