document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082287>Question 1082287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for the ellipse, satisfying the following conditions. Foci at (0,-2) and (0,2); the point (3,2) on the ellipse  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696339 by </B><A HREF=/tutors/aboutme.mpl?userid=natolino_2017><B>natolino_2017(77)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=natolino_2017><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=696339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mid point between the two focus is the center of the ellipse.\r<BR>\n" );
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document.write( "In this case, Center= ((0+0)/2 , (2+-2)/2) =(0 , 0).\r<BR>\n" );
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document.write( "Let P = (3 , 2), F1 = (0 , -2), F2 =(0 , 2)\r<BR>\n" );
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document.write( "\"The sum of the distance of a point of the ellipse to every Focus, is constant and equal to the double of the Semi-major axis (A)\"\r<BR>\n" );
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document.write( "PF1 + PF2 = 2A.\r<BR>\n" );
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document.write( "5 + 3 = 2A\r<BR>\n" );
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document.write( "A = 4\r<BR>\n" );
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document.write( "Let C: distance from the center to a focus.\r<BR>\n" );
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document.write( "   C = 2.\r<BR>\n" );
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document.write( "A^2 = B^2 + C^2\r<BR>\n" );
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document.write( "   B = sqrt(12).\r<BR>\n" );
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document.write( "So the equation is\r<BR>\n" );
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document.write( " x^2/12 + y^2/16 = 1.\r<BR>\n" );
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document.write( "observation: the Focus doesn't belong to the ellipse.\r<BR>\n" );
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document.write( "@natolino_  </SPAN>\n" );
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