document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162020>Question 162020</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 11. What is the center of the ellipse whose equation is (x^2)/25 + (y^2)/4 = 1? \r<BR>\n" );
document.write( "\n" );
document.write( "A (25,1)<BR>\n" );
document.write( "B (5,1)<BR>\n" );
document.write( "C (4,25)<BR>\n" );
document.write( "D (4,1)<BR>\n" );
document.write( "E (0,0)<BR>\n" );
document.write( "F (5,2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x-h)^2 / a^2   +   (y-k)^2 / b^2 = 1 I tried to used this equation to help, but im really stuck. I appericaite any help you can offer. Thank you!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119403 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=119403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have the right idea, but it might help to go even further\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F25+%2B+%28y%5E2%29%2F4+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F25+%2B+%28y%5E2%29%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2F25+%2B+%28y-0%29%5E2%2F4+=+1 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2F25+%2B+%28y-0%29%5E2%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-0 ALIGN=MIDDLE  ALT=\"x-0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-0 ALIGN=MIDDLE  ALT=\"y-0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is possible since adding/subtracting zero doesn't affect the equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2F5%5E2+%2B+%28y-0%29%5E2%2F2%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2F5%5E2+%2B+%28y-0%29%5E2%2F2%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2 ALIGN=MIDDLE  ALT=\"5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how the equation above fits the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2+%2F+a%5E2+%2B+%28y-k%29%5E2+%2F+b%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2+%2F+a%5E2+%2B+%28y-k%29%5E2+%2F+b%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > where in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=5 ALIGN=MIDDLE  ALT=\"a=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Remember the center is simply (h,k). So this means that the center is (0,0). So the answer is E\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: If you are really stuck, you can solve for \"y\" and graph. Once you do that, you'll see that the center is at (0,0) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );