document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619455>Question 619455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have the equation :  <BR>\n" );
document.write( "(y+5)^2/6^2-(x-2)^2/5^2=1\r<BR>\n" );
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document.write( "i need to identify the vertices and foci of the hyperbola.  I'm not sure how to do that with my numerators.  And I also need to graph this.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389726 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=389726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (y+5)^2/6^2-(x-2)^2/5^2=1 <BR>\n" );
document.write( "i need to identify the vertices and foci of the hyperbola. I'm not sure how to do that with my numerators. And I also need to graph this<BR>\n" );
document.write( "**<BR>\n" );
document.write( "Given 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: (2,-5)<BR>\n" );
document.write( "a=6<BR>\n" );
document.write( "a^2=36<BR>\n" );
document.write( "Vertices: (2,-5±a)=(2,-5±6)=(2,-11) and (2,1)<BR>\n" );
document.write( "b=5<BR>\n" );
document.write( "b^2=25<BR>\n" );
document.write( "c^2=a^2+b^2=36+25=61<BR>\n" );
document.write( "c=&#8730;61&#8776;7.8<BR>\n" );
document.write( "Foci:  (2,-5±c)=(2,-5±7.8)=(2,-12.8) and (2,2.8)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Slopes of asymptotes for hyperbolas with vertical transverse axis=a/b=6/5<BR>\n" );
document.write( "Asymptotes are straight lines that intersect at the center: Equation: y=mx+b, m=slope, b=y-intercept<BR>\n" );
document.write( "Equation for asymptote with slope<0: y=-6x/5+b<BR>\n" );
document.write( "solve for b using coordinates of center (2,-5)<BR>\n" );
document.write( "-5=-6*2/5+b<BR>\n" );
document.write( "-5=-12/5+b<BR>\n" );
document.write( "b=-5+12/5=-25/5+12/5=-13/5<BR>\n" );
document.write( "Equation: y=-6x/5-13/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation for asymptote with slope>0: y=6x/5+b<BR>\n" );
document.write( "solve for b using coordinates of center (2,-5)<BR>\n" );
document.write( "-5=6*2/5+b<BR>\n" );
document.write( "-5=12/5+b<BR>\n" );
document.write( "b=-5-12/5=-25/5-12/5=-37/5<BR>\n" );
document.write( "Equation: y=6x/5-37/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(36+36(x-2)^2/25)^.5-5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C%2836%2B36%28x-2%29%5E2%2F25%29%5E.5-5%2C-%2836%2B36%28x-2%29%5E2%2F25%29%5E.5-5%2C%0D%0A-6x%2F5-13%2F5%2C6x%2F5-37%2F5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );