document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83900>Question 83900</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201812525/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Name the center,foci,and the vertics of each ellipse whose equation is given\r<BR>\n" );
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document.write( "(x-3)^2/25 + (y-4)^2/16 =1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60387 by </B><A HREF=/tutors/aboutme.mpl?userid=chitra><B>chitra(359)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chitra><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The given equation is:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%5E2%2F25%29+%2B+%28%28y-4%29%5E2%2F16%29+=+1 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%5E2%2F25%29+%2B+%28%28y-4%29%5E2%2F16%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Comparing this to the standard equation, we get:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x+-+h%29%5E2%2Fa%5E2%29+%2B+%28%28y+-+k%29%5E2%2Fb%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"%28%28x+-+h%29%5E2%2Fa%5E2%29+%2B+%28%28y+-+k%29%5E2%2Fb%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "We find that the centre of the ellipse given by (h,k) is equal to (3, 4) \r<BR>\n" );
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document.write( "The foci of the Ellipse is given by (+- ae, 0) \r<BR>\n" );
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document.write( "So we first find the eccentricity using the formula: \r<BR>\n" );
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document.write( "e =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%281+-+%28b%5E2%2Fa%5E2%29%29+ ALIGN=MIDDLE  ALT=\"+sqrt%281+-+%28b%5E2%2Fa%5E2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "e = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%281+-+16%2F25%29%29+ ALIGN=MIDDLE  ALT=\"+sqrt%281+-+16%2F25%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "e = 3/5 \r<BR>\n" );
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document.write( "So now focus is:  (+- ae, 0)  = (+ -3, 0) \r<BR>\n" );
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document.write( "Now the vertex is (+ - a, 0)  = (+-  5, 0) \r<BR>\n" );
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document.write( "hence, the solution </SPAN>\n" );
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