document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471709>Question 471709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation in standard form of an ellipse with center at (0,0) minor axis of length 18, and foci at (0,-12) and (0,12).\r<BR>\n" );
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document.write( "a. (x^2/225)+(y^2/81)=1<BR>\n" );
document.write( "b. (x^2/144)+(y^2/81)=1<BR>\n" );
document.write( "c. (x^2/81)+(y^2/225)=1<BR>\n" );
document.write( "d. (x^2/9)+(y^2/15)=1<BR>\n" );
document.write( "e. (x^2/15)+(y^2/9)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #333602 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=333602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation in standard form of an ellipse with center at (0,0) minor axis of length 18, and foci at (0,-12) and (0,12). <BR>\n" );
document.write( "a. (x^2/225)+(y^2/81)=1<BR>\n" );
document.write( "b. (x^2/144)+(y^2/81)=1<BR>\n" );
document.write( "c. (x^2/81)+(y^2/225)=1<BR>\n" );
document.write( "d. (x^2/9)+(y^2/15)=1<BR>\n" );
document.write( "e. (x^2/15)+(y^2/9)=1<BR>\n" );
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document.write( "Based on given data, this is an equation of an ellipse with vertical major axis of the standard form: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the center.<BR>\n" );
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document.write( "Normally, a complete solution would be required, but because this is a multiple choice question, we can save some steps in determining the correct answer. (Assuming one of the choices is a correct answer)<BR>\n" );
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document.write( "First, since the center is at (0,0), h and k will not appear in the equation.<BR>\n" );
document.write( "Since this ellipse has a vertical major axis, a^2,  the larger number will appear under the y-term.<BR>\n" );
document.write( "Given length of minor axis=18=2b<BR>\n" );
document.write( "b=9<BR>\n" );
document.write( "b^2=81 (this is the smaller number that should be under the x-term)<BR>\n" );
document.write( "From this information we can conclude that c. (x^2/81)+(y^2/225)=1 is the right answer.<BR>\n" );
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document.write( "Calculating a^2 is not necessary for selecting the right multiple choice, but if required, this is how you can do it:<BR>\n" );
document.write( "Foci:<BR>\n" );
document.write( "c=distance from center to one focal point=12<BR>\n" );
document.write( "c^2=144<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "a^2=c^2+b^2=144+81=225 </SPAN>\n" );
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