document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=545573>Question 545573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, could you please help me figure out where I am going wrong with the foci and vertices of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25x%5E2-4y%5E2%2B50x%2B16y=+91+ ALIGN=MIDDLE  ALT=\"+25x%5E2-4y%5E2%2B50x%2B16y=+91+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I keep getting an \"a\" of 2 and a \"b\" of 5 (with \"c\" being sqrt( 29 ) ) but my calculator's graph says it should be different (an \"a\" of 1/2). Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #355731 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=355731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find Foci and Vertices<BR>\n" );
document.write( "25x^2-4y^2+50x+16y= 91<BR>\n" );
document.write( "**<BR>\n" );
document.write( "25x^2+50x+-4y^2+16y= 91<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "25(x^2+2x+1)-4(y^2-4y+4)= 91+25-16=100<BR>\n" );
document.write( "25(x+1)^2-4(y-2)^2=100<BR>\n" );
document.write( "divide by 100<BR>\n" );
document.write( "(x+1)^2/4-(y-2)^2/25=1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis of the standard form:<BR>\n" );
document.write( "(x-h)^2/a^2-(y-k)^2/b^2=1<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "center:(-1,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "vertices: (-1±a, 2)=(-1±2,2)=(-3,2) and (1,2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=25<BR>\n" );
document.write( "b=5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=4+25=29<BR>\n" );
document.write( "c=&#8730;29&#8776;5.4<BR>\n" );
document.write( "Foci: (-1±&#8730;29,2), (-1±6.4,2)=(-7.4,2) and (5.4,2)\r<BR>\n" );
document.write( "\n" );
document.write( "Seems like you got a, b, and c correct. Maybe you did not punched the right data into your graphing calculator. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );