document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=603022>Question 603022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes. <BR>\n" );
document.write( "Vertices: (5,19),(5,-5)<BR>\n" );
document.write( "Foci: (5,20),(5,-6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380560 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=380560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the information provided to write the standard form equation of each hyperbola, give me a,b,c and the asymptotes. <BR>\n" );
document.write( "Vertices: (5,19),(5,-5)<BR>\n" );
document.write( "Foci: (5,20),(5,-6)<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Information given shows hyperbola has a vertical transverse axis:<BR>\n" );
document.write( "Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given hyperbola:<BR>\n" );
document.write( "center: (5,7)<BR>\n" );
document.write( "length of vertical transverse axis=24=2a<BR>\n" );
document.write( "a=12<BR>\n" );
document.write( "a^2=144<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c=13<BR>\n" );
document.write( "c^2=169<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "b^2=c^2-a^2=169-144=25<BR>\n" );
document.write( "b=&#8730;25=5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "asymptotes:<BR>\n" );
document.write( "Asymptotes are straight lines which go thru center<BR>\n" );
document.write( "Standard form: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "slope=±a/b=±12/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=12x/5+b<BR>\n" );
document.write( "solving for b using coordinates of center<BR>\n" );
document.write( "7=12*5/5+b<BR>\n" );
document.write( "b=-12+7=5<BR>\n" );
document.write( "y=12x/5-5<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "y=-12x/5+b<BR>\n" );
document.write( "solving for b using coordinates of center<BR>\n" );
document.write( "7=-12*5/5+b<BR>\n" );
document.write( "b==12+7=19<BR>\n" );
document.write( "y==12x/5+19<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of given hyperbola:<BR>\n" );
document.write( " (y-7)^2/144-(x-5)^2/25=1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );