document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30463>Question 30463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (M) Question: <BR>\n" );
document.write( "Find the center, vertices, and foci for the ellipse:<BR>\n" );
document.write( "4x^2+16y^2=64\r<BR>\n" );
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document.write( "(A) center (0,0) vertices (0, +4) foci (0, +3.5)<BR>\n" );
document.write( "(B) center (2, 4) vertices (4, 0) and (4,8) foci (4, -1.5) and (4, 5.5)<BR>\n" );
document.write( "(C) center (0,0) vertices (+4, 0) foci (+3.5,0)<BR>\n" );
document.write( "(D) center (4,2) vertices (0,2) and (4,2) foci (0.5,2) and (7.5,2)\r<BR>\n" );
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document.write( "Please be specific as to whcih letter is correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17104 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=17104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^2+16y^2=64<BR>\n" );
document.write( "Dividing by 64<BR>\n" );
document.write( "x^2/16 +y^2/4 = 1<BR>\n" );
document.write( "That is x^2/(4^2) +y^2/(2^2) = 1 ----(1)<BR>\n" );
document.write( "which is in the standard form x^2/a^2 +y^2/b^2 = 1 (with a>b)<BR>\n" );
document.write( "The major axis is the x-axis <BR>\n" );
document.write( "and the minor axis is the y-axis<BR>\n" );
document.write( "Hence Centre C= (0,0)<BR>\n" );
document.write( "semi-major length = a = 4 and <BR>\n" );
document.write( "semi-minor length = b = 2<BR>\n" );
document.write( "The vertices are A(4,0) and A'(-4,0) on the major axis <BR>\n" );
document.write( "and B(0,2) and B'(0,-2) on the minor axis.<BR>\n" );
document.write( "To find the eccentricity e we use the formula<BR>\n" );
document.write( "b^2 = a^2(1-e^2)<BR>\n" );
document.write( "4 = 16(1-e^2)<BR>\n" );
document.write( "1 = 4(1-e^2) (dividing by 4)<BR>\n" );
document.write( "1 = 4 - 4e^2<BR>\n" );
document.write( "4e^2 = 4-1<BR>\n" );
document.write( "4e^2 = 3<BR>\n" );
document.write( "4e^2 = 4-1<BR>\n" );
document.write( "4e^2 = 3<BR>\n" );
document.write( "e^2= 3/4<BR>\n" );
document.write( "Therefore e = [sqrt(3)]/2  (taking the positive sqrt as e > 0) <BR>\n" );
document.write( "The foci are given by S(ae,0) and S'(-ae,0)<BR>\n" );
document.write( "And (ae) = 4X(rt(3)]/2 = 2(sqrt(3))<BR>\n" );
document.write( "Therefore the foci are <BR>\n" );
document.write( "S(ae,0)= S(2(rt3),0) and S'(-ae,0)=(-2(rt3),0)\r<BR>\n" );
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document.write( "Remark: We are asked to give center, vertices(notice the plural) <BR>\n" );
document.write( "and the foci(notice the plural) and in the answer set only one vertex and one focus given along with the center<BR>\n" );
document.write( "The choice (C) is close to the answer\r<BR>\n" );
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document.write( " </SPAN>\n" );
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