document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=732377>Question 732377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the equation of a hyperbola, find the standard equation, vertices, foci, asymptotes, and graph<BR>\n" );
document.write( "1) (x^2/36)- (y^2/49)=1\r<BR>\n" );
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document.write( "2) 25x^2-16y^2-400=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448069 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=448069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for the equation of a hyperbola, find the standard equation, vertices, foci, asymptotes, and graph<BR>\n" );
document.write( "1) (x^2/36)- (y^2/49)=1 <BR>\n" );
document.write( "2) 25x^2-16y^2-400=0<BR>\n" );
document.write( "***<BR>\n" );
document.write( "Standard form of equation for a hyperbola with horizontal transverse axis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%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( "1) (x^2/36)- (y^2/49)=1<BR>\n" );
document.write( "center:(0,0)<BR>\n" );
document.write( "a^2=36<BR>\n" );
document.write( "a=&#8730;36=6<BR>\n" );
document.write( "vertices: (0±a,0)=(0±6,0)=(6,0) and (-6,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=49<BR>\n" );
document.write( "b=&#8730;49=7<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=36+49=85<BR>\n" );
document.write( "c=&#8730;85&#8776;9.2<BR>\n" );
document.write( "foci: (0±c,0)=(0±9.2,0)=(9.2,0) and (-9.2,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "slopes of asymptotes=±b/a=±7/6<BR>\n" );
document.write( "Equation of asymptote with slope,m=7/6<BR>\n" );
document.write( "y=7x/6<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with slope,m=-7/6<BR>\n" );
document.write( "y=-7x/6\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "see graph below:<BR>\n" );
document.write( "y=±(49x^2/36-49)^.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+-10%2C10%2C+-10%2C+10%2C%2849x%5E2%2F36-49%29%5E.5%2C-%2849x%5E2%2F36-49%29%5E.5%2C7x%2F6%2C-7x%2F6%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I will let you do the 2nd problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );