document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=616686>Question 616686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci.<BR>\n" );
document.write( "(x-3)^2/9 - (y+5)^2/16 = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387846 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=387846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci.<BR>\n" );
document.write( "(x-3)^2/9 - (y+5)^2/16 = 1<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Equation is that of a hyperbola with vertical transverse axis.<BR>\n" );
document.write( "Its standard form: (y-k)^2/a^2-(x-h)^2/b^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( "vertices: (0, 0±a)=(0,0±4)=(0,-4) and (0,4)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=&#8730;9=3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=16+9=25<BR>\n" );
document.write( "c=&#8730;25=5<BR>\n" );
document.write( "foci:(0, 0±c)=(0,0±5)=(0,-5) and (0,5)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "slopes of asymptotes with vertical transverse axis=±a/b=±4/3<BR>\n" );
document.write( "asymptotes are straight lines which intersect at the center.<BR>\n" );
document.write( "equation:y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "y-intercept=0, since asymptotes go thru the origin(0,0)<BR>\n" );
document.write( "equation of asymptote with negative slope: y=-4x/3<BR>\n" );
document.write( "equation of asymptote with positive slope: y=4x/3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(16+16x^2/9)^.5\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );