document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=676440>Question 676440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need the general equation for this ellipse and its major axis.<BR>\n" );
document.write( "4x^2+y^2+4y=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420367 by </B><A HREF=/tutors/aboutme.mpl?userid=khurshidi><B>khurshidi(7)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khurshidi><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=khurshidi><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need the general equation for this ellipse and its major axis.<BR>\n" );
document.write( "4x^2+y^2+4y=0\r<BR>\n" );
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document.write( "Solution:\r<BR>\n" );
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document.write( "4x^2 + y^2 + 4y = 0 \r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "4x^2 + 0x + y^2 + 4y = 0 -------->(1)\r<BR>\n" );
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document.write( "Adding '4' on both sides in (1)\r<BR>\n" );
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document.write( "4x^2 + 2(4x)(0) + 0^2 + y^2 + 4y + 4 = 4\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "4(x + 0)^2 + (y + 2)^2 = 4\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "4(x + 0)^2/4 + (y + 2)^2/4 = 1\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "(x + 0)^2/1 + (y + 2)^2/4 = 1\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "(x + 0)^2/1^2 + (y + 2)^2/2^2 = 1 -------->(2)\r<BR>\n" );
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document.write( "Compare (2) with general equation of the ellipse\r<BR>\n" );
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document.write( "(x - h)^2/a^2 + (y - k)^2/b^2 = 1\r<BR>\n" );
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document.write( "we get\r<BR>\n" );
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document.write( "Center(h, k) = (0, -2)\r<BR>\n" );
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document.write( "since\r<BR>\n" );
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document.write( "b > a<BR>\n" );
document.write( "i.e. 2 > 1\r<BR>\n" );
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document.write( "therefore major axis along y-axis<BR>\n" );
document.write( "thus<BR>\n" );
document.write( "c^2 = b^2 - a^2 = 2^2 - 1^2 = 4 - 1 = 3\r<BR>\n" );
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document.write( "c^2 = 3\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "c = (+-)sqrt(3)\r<BR>\n" );
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document.write( "Thus\r<BR>\n" );
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document.write( "foci(h, k(+-)c) = (0, -2(+-)sqrt(3))\r<BR>\n" );
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document.write( "langht of major axis = 2b = 2 * 2 = 4\r<BR>\n" );
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document.write( "Hence<BR>\n" );
document.write( "Equation (2) is the general equation of the given ellipse with center C(h, k) = (0, -2) and its major axis is along y-axis and length of major axis is 4units.\r<BR>\n" );
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document.write( "Hope the answer your question\r<BR>\n" );
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document.write( "Regards,<BR>\n" );
document.write( "Khurshidi<BR>\n" );
document.write( "http://sscom.netai.net<BR>\n" );
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