document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636453>Question 636453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center, foci, vertices, and asymptotes. Please show all your steps.\r<BR>\n" );
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document.write( "y^2/25-x^2=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401044 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=401044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the center, foci, vertices, and asymptotes. Please show all your steps. <BR>\n" );
document.write( "y^2/25-x^2=1<BR>\n" );
document.write( "**<BR>\n" );
document.write( "This is a hyperbola with vertical transverse axis.<BR>\n" );
document.write( "Its standard form of equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation of a hyperbola:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F25-x%5E2=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F25-x%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "a=&#8730;25=5<BR>\n" );
document.write( "vertices: (0, 0±a)=(0, 0±5)=(0,-5) and (0,5)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=25+1=26<BR>\n" );
document.write( "c=&#8730;26&#8776;5.1<BR>\n" );
document.write( "Foci:  (0, 0±c)=(0, 0±5.1)=(0,-5.1) and (0,5.1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes are lines that intersect at center (0,0). Equation: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "slopes of asymptotes of hyperbolas with vertical transverse axis=±a/b=±5/1=±5<BR>\n" );
document.write( "Equation of asymptote with negative slope (-5)<BR>\n" );
document.write( "y=-5x+b<BR>\n" );
document.write( "y=-5x+0<BR>\n" );
document.write( "y=-5x<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with positive slope (5)<BR>\n" );
document.write( "y=5x+b<BR>\n" );
document.write( "y=5x+0<BR>\n" );
document.write( "y=5x<BR>\n" );
document.write( " </SPAN>\n" );
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