document.write( "Question 1087920: Find the center, vertices, foci and eccentricity of the ellipse x^2+9y^2=36. \n" ); document.write( "
Algebra.Com's Answer #702212 by ikleyn(52797)\"\" \"About 
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document.write( "\"x%5E2+%2B+9y%5E2\" = \"36\"  is equivalent to  \"x%5E2%2F36\" + \"y%5E2%2F4\" = \"1\"\r\n" );
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document.write( "The center is at (0,0), the origin of the coordinate center.\r\n" );
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document.write( "The major axis is along the x-axis, while the minor axis is along the y-axis.\r\n" );
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document.write( "The major axis is  a = 6 = \"sqrt%2836%29\" units long.\r\n" );
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document.write( "The minor axis is  b = 2 = \"sqrt%284%29\" units long.\r\n" );
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document.write( "The vertices are (6,0) and (-6,0), while the co-vertices are (0,2) and (0,-2).\r\n" );
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document.write( "The linear eccentricity is \"c\" = \"sqrt%28a%5E2+-+b%5E2%29\" = \"sqrt%286%5E2+-+2%5E2%29\" = \"sqrt%2832%29\" = \"4%2Asqrt%282%29\".\r\n" );
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document.write( "The foci of the ellipse are  (\"-4%2Asqrt%282%29\",\"0\")  and  (\"4%2Asqrt%282%29\",\"0\").\r\n" );
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\n" ); document.write( "\n" ); document.write( "Figure. Ellipse \"x2%2F36\" + \"y%5E2%2F4\" = 1\r
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\n" ); document.write( "\n" ); document.write( "See the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Ellipse definition, canonical equation, characteristic points and elements \r
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\n" ); document.write( "\n" ); document.write( "    - Standard equation of an ellipse\r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of an ellipse given by its standard equation\r
\n" ); document.write( "\n" ); document.write( "    - Find the standard equation of an ellipse given by its elements\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Ellipses. Definition, major elements and properties. Solved problems\".\r
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