document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856652>Question 856652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of hyperbola H is \r<BR>\n" );
document.write( "\n" );
document.write( "(x+4)^2/64 - (y+3)^3/16 = 1\r<BR>\n" );
document.write( "\n" );
document.write( "What are the asymptotes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516168 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=516168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of hyperbola H is <BR>\n" );
document.write( "(x+4)^2/64 - (y+3)^3/16 = 1 <BR>\n" );
document.write( "What are the asymptotes?<BR>\n" );
document.write( "***<BR>\n" );
document.write( "Given hyperbola has a 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;\" ><BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "center: (-4,-3)<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "a=8<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "b=4:<BR>\n" );
document.write( "asymptotes are equations of straight lines of standard form: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "slopes=±b/a=±4/8=±1/2<BR>\n" );
document.write( "asymptotes go thru center(-4,-3)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with slope<0<BR>\n" );
document.write( "y=-x/2+b<BR>\n" );
document.write( "solve for b using coordinates of center<BR>\n" );
document.write( "-3=-(-4)/2+b<BR>\n" );
document.write( "b=-5<BR>\n" );
document.write( "equation:y=-x/2-5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with slope>0<BR>\n" );
document.write( "y=x/2+b<BR>\n" );
document.write( "solve for b using coordinates of center<BR>\n" );
document.write( "-3=-4)/2+b<BR>\n" );
document.write( "b=-1<BR>\n" );
document.write( "equation:y=x/2-1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );