document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=448306>Question 448306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> need to find the center and forci and the lengths of major axes and minor axes for the ellipse and graph it \r<BR>\n" );
document.write( "\n" );
document.write( "x^2 + 25y^2 -8x + 100y+91=0\r<BR>\n" );
document.write( "\n" );
document.write( "Show me how to do it dont just give me the answer please:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #308561 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=308561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> need to find the center and forci and the lengths of major axes and minor axes for the ellipse and graph it <BR>\n" );
document.write( "x^2 + 25y^2 -8x + 100y+91=0 <BR>\n" );
document.write( "Show me how to do it dont just give me the answer please:)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)<BR>\n" );
document.write( "Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1 (a>b)<BR>\n" );
document.write( "x^2 + 25y^2 -8x + 100y+91=0<BR>\n" );
document.write( "completing the square<BR>\n" );
document.write( "(x^2-8x+16)+25(y^2+4y+4)=-91+16+100=25<BR>\n" );
document.write( "(x-4)^2+25(y+2)^2=25<BR>\n" );
document.write( "divide by 25<BR>\n" );
document.write( "(x-4)^2/25+(y+2)^2/1=1<BR>\n" );
document.write( "This is an ellipse with center at (4,-2) and a horizontal major axis. (standard form first listed above)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "a=5<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "c^2=a^2-b^2=5-1=4<BR>\n" );
document.write( "c=2<BR>\n" );
document.write( "Length of major axis = 2a=10<BR>\n" );
document.write( "End points of major axis, (9,-2), (-1,-2) (also, called the vertices)<BR>\n" );
document.write( "Length of minor axis=2b=2<BR>\n" );
document.write( "End points of minor axis, (4,-3), (4,-1)<BR>\n" );
document.write( "Foci,(2,-2), (6-2)<BR>\n" );
document.write( "See graph below for visual evidence of parameters above<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=(1-(x-4)^2/25)^.5-2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%281-%28x-4%29%5E2%2F25%29%5E.5-2%2C-%281-%28x-4%29%5E2%2F25%29%5E.5-2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );