document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=46052>Question 46052</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618501401/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to find the center, vertices, and foci of the ellipse of the following equation:\r<BR>\n" );
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document.write( "x^2/49 + y^2/36 = 1\r<BR>\n" );
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document.write( "Any help will be greatly appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #30560 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=30560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> --------------------------------------------------------<BR>\n" );
document.write( "I am trying to find the center, vertices, and foci of the ellipse of the following equation:<BR>\n" );
document.write( "x^2/49 + y^2/36 = 1 <BR>\n" );
document.write( "STANDARD EQN.OF ELLIPSE IS<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ax+%2B+a%5B12%5D%2Ay+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ax+%2B+a%5B22%5D%2Ay+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++x+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++y+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++x+=+%282%2A-1+-+0%2A1%29%2F%281%2A-1-1%2A1%29+=+1%2C%0D%0A++++++y+=+%281%2A0+-+1%2A2%29%2F%281%2A-1-1%2A1%29+=+1%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (x=1, y=1}<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "(X-H)^2/A^2 +(Y-K)^2/B^2=1<BR>\n" );
document.write( "CENTRE IS (H,K)..AS PER THE PROBLEM H=0.....K=0 HENCE CENTRE OF ELLIPSE IS AT<BR>\n" );
document.write( "IS (0,0)<BR>\n" );
document.write( "A=SQRT(49)=7........B=SQRT(36)=6<BR>\n" );
document.write( "WHERE MAJOR AXIS =2A=2*7=14...MINOR AXIS =2B=2*6=12<BR>\n" );
document.write( "ECCENTRICITY =E =SQRT{(A^2-B^2)/A^2}=SQRT{(49-36)/49}=SQRT(13)/7<BR>\n" );
document.write( "FOCI ARE GIVEN BY....(H+AE,K),(H-AE,K)<BR>\n" );
document.write( "(SQRT(13),0),(-SQRT(13),0)<BR>\n" );
document.write( "VERTICES ARE (H,K+B),(H,K-B)=(0,6),(0,-6)<BR>\n" );
document.write( "AND....(H+A,K),(H-A,K)=(7,0),(-7,0) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );