document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=618962>Question 618962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equations of the asymptotes of the hyperbola.\r<BR>\n" );
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document.write( "25y^2 - 16x -400 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389204 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=389204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equations of the asymptotes of the hyperbola. <BR>\n" );
document.write( "25y^2 - 16x^2 -400 = 0<BR>\n" );
document.write( "25y^2-16x^2=400<BR>\n" );
document.write( "Divide by 400<BR>\n" );
document.write( "y^2/16-x^2/25=1<BR>\n" );
document.write( "This  is an equation of a hyperbola with vertical transverse axis<BR>\n" );
document.write( "Its form of equation: (y-k)^2/a^2-(x-h)^2=1, (h,k)=(x,y) coordinates of the center.<BR>\n" );
document.write( "For given equation: <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( "b^2=25<BR>\n" );
document.write( "b=&#8730;25=5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes are straight lines that intersect at the center(0,0). Equation: y=mx+b, m=slope, b=y intercept<BR>\n" );
document.write( "Slopes of asymptotes for hyperbolas with vertical transverse axis=a/b=4/5<BR>\n" );
document.write( "Equation of asymptote with slope<0<BR>\n" );
document.write( "y=-4x/5+b<BR>\n" );
document.write( "since asymptote go thru center, y-intercept, b=0<BR>\n" );
document.write( "so, equation: y=-4x/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "By the same reasoning,<BR>\n" );
document.write( "Equation of asymptote with slope>0<BR>\n" );
document.write( "y=4x/5<BR>\n" );
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