document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=930815>Question 930815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertices, foci, and eccentricity of the ellipse. Determine the lengths of the major and minor axes, and sketch the graph.<BR>\n" );
document.write( "1. 4x^2+25y^2=100\r<BR>\n" );
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document.write( "2. x^2/16+y^2/25=1\r<BR>\n" );
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document.write( "3. 1/2x^2+1/8y^2=1/4\r<BR>\n" );
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document.write( "4. y^2=1-2x^2\r<BR>\n" );
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document.write( "5. X^2+4y^2=16<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #565302 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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/cgi-bin/show-face.mpl?user=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=565302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Standard Form of an Equation of an Ellipse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+ ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "where Pt(h,k) is the center. (a variable positioned to correspond with major axis)<BR>\n" );
document.write( " a and b  are the respective vertices distances from center.<BR>\n" );
document.write( " The foci distances from center:   c = ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2-b%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2-b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where  a > b<BR>\n" );
document.write( "eccentricity = c/a<BR>\n" );
document.write( ".........<BR>\n" );
document.write( "4x^2+25y^2=100 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F5%5E2+%2B+y%5E2%2F2%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F5%5E2+%2B+y%5E2%2F2%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > C(0,0)<BR>\n" );
document.write( "V(5,0),V(-5,0) & V(0,2),V(0,-2)<BR>\n" );
document.write( "c =&#8730;(25 - 4) = &#8730;(21)<BR>\n" );
document.write( "eccentricity = &#8730;21/5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+++-10%2C10%2C-10%2C10%2C++arc%280%2C0%2C10%2C4%29%2C+%0D%0A+grid%281%29%2C%0D%0A%0D%0Agraph%28+300%2C+300%2C+-10%2C10%2C-10%2C10%2C0+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "..........<BR>\n" );
document.write( "x^2/16+y^2/25=1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4%5E2+%2B+y%5E2%2F5%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4%5E2+%2B+y%5E2%2F5%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  C(0,0)<BR>\n" );
document.write( " & V(4,0),V(-4,0) & V(0,5),V(0,-5)\r<BR>\n" );
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document.write( " c =&#8730;(25 - 16) = 3<BR>\n" );
document.write( "eccentricity = 3/5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+++-10%2C10%2C-10%2C10%2C++arc%280%2C0%2C8%2C10%29%2C+%0D%0A+grid%281%29%2C%0D%0Agraph%28+300%2C+300%2C+-10%2C10%2C-10%2C10%2C0+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........<BR>\n" );
document.write( "1/2x^2+1/8y^2=1/4 <BR>\n" );
document.write( "2x^2 + y^2/4 = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%28sqrt%281%2F2%29%29%5E2+%2B+y%5E2%2F+2%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F%28sqrt%281%2F2%29%29%5E2+%2B+y%5E2%2F+2%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".........<BR>\n" );
document.write( "y^2=1-2x^2 <BR>\n" );
document.write( "2x^2 + y^2 = 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F%28sqrt%281%2F2%29%29%5E2+%2B+y%5E2%2F1%5E2+=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F%28sqrt%281%2F2%29%29%5E2+%2B+y%5E2%2F1%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".......<BR>\n" );
document.write( "X^2+4y^2=16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4%5E2+%2B+y%5E2%2F2%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4%5E2+%2B+y%5E2%2F2%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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