document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48302>Question 48302</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534423272/algebrahomeworkh>College Algebra </A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I need help, I can't seem to grasp this concept.  The question is.. identify the center, vertices, foci, and equations of the asymptotes of the hyperbola:   25y^2 - 9x^2 - 100y - 54x - 206 = 0.  If you can help it would be greatly appreciated. Thank you lots.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #31949 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=31949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need help, I can't seem to grasp this concept. The question is.. identify the center, vertices, foci, and equations of the asymptotes of the hyperbola: 25y^2 - 9x^2 - 100y - 54x - 206 = 0. If you can help it would be greatly appreciated. <BR>\n" );
document.write( "----------------------------------------------------------------------------------<BR>\n" );
document.write( "FIRST COMPLETE SQUARES<BR>\n" );
document.write( "25(Y^2-4y)-9(X^2+6X)-206=0<BR>\n" );
document.write( "25{Y^2-2*Y*2+2^2-2^2}-9{X^2+2*X*3+3^2-3^2}-206=0<BR>\n" );
document.write( "25(Y-2)^2-100-9(X+3)^2+81-206=0<BR>\n" );
document.write( "-9(X+3)^2+25(Y-2)^2=-81+100+206=225<BR>\n" );
document.write( "-[{(X+3)^2}/(225/9)]+[{(Y-2)^2}/(225/25)]=1<BR>\n" );
document.write( "[(Y-2)^2/5^2]-[(X+3)^2/3^2]=1<BR>\n" );
document.write( "NOW<BR>\n" );
document.write( "SEE THE FOLLOWING AND YOU SHOULD BE ABLE TO SOLVE YOUR PROBLEM BY YOUR SELF..<BR>\n" );
document.write( "Quadratic-relations-and-conic-sections/28184: What is the vertices,<BR>\n" );
document.write( "foci, and slope of the asymptotes for the hyperbola whose equation is,<BR>\n" );
document.write( "y^2/16 - x^2/25 =25?<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 15970 by venugopalramana(1088) About Me  on 2006-03-04 03:12:07<BR>\n" );
document.write( "(Show Source):<BR>\n" );
document.write( "SEE THE FOLLOWING AND YOU SHOULD BE ABLE TO SOLVE YOUR PROBLEM BY YOUR SELF.....<BR>\n" );
document.write( "THE ANSWERS FOR YOUR CASE...H=0...K=0..A=4...B=5....EQN IS OF THE TYPE<BR>\n" );
document.write( "(Y-K)^2/B^2-(X-H)^2/A^2=1....<BR>\n" );
document.write( "SO VERTICES ARE...(H,(K-B)) AND (H,(K+B)) ...(0,-5) AND (0,5)<BR>\n" );
document.write( "FOCI ARE {H,(K-BE)} AND {H,(K+BE)}...WHERE E IS<BR>\n" );
document.write( "ECCENTRICITY =SQRT{(A^2+B^2)/B^2}=SQRT((16+25)/25)=SQRT(41/25)<BR>\n" );
document.write( "SO FOCI ARE =(0,-5SQRT(41/25) AND (0,5SQRT(41/25)...<BR>\n" );
document.write( "OR....(0,-SQRT(41)) AND (0,SQRT(41)<BR>\n" );
document.write( "ASYMPTOTES ARE GIVEN BY<BR>\n" );
document.write( "Y^2/16-X^2/25=K<BR>\n" );
document.write( "25Y^2-16X^2-400K=0<BR>\n" );
document.write( "(5Y+4X+A)(5Y-4X+B)=0<BR>\n" );
document.write( "SLOPES OF ASYMPTOTES ARE<BR>\n" );
document.write( "-4/5 AND 4/5<BR>\n" );
document.write( "THE GRAPHS LOOK LIKE THIS<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A4%2A%281%2Bx%5E2%2F25%29%5E0.5%2C-4%2A%281%2Bx%5E2%2F25%29%5E0.5%2C4%2Ax%2F5%2C-4%2Ax%2F5+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );