document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=596617>Question 596617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the equation for the following asymptotes for the following hyperbola x^2-4y^2=16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #377814 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=377814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> write the equation for the following asymptotes for the following hyperbola x^2-4y^2=16<BR>\n" );
document.write( "divide by 16<BR>\n" );
document.write( "x^2/16-y^2/4=1<BR>\n" );
document.write( "This is an equation for a hyperbola with horizontal transverse axis of the standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center.<BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "center:(0,0)<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=&#8730;16=4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=4<BR>\n" );
document.write( "b=2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slopes of asymptotes, m: ±b/a=±2/4=±1/2<BR>\n" );
document.write( "equations of asymptotes:<BR>\n" );
document.write( "y=mx+b and y=-mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "y=x/2+b and y=-x/2+b<BR>\n" );
document.write( "since asymptotes go thru origin, (0,0), y-intercept,b=0<BR>\n" );
document.write( "equations therefore are:<BR>\n" );
document.write( "y=x/2 and y=-x/2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );