document.write( "Question 1084952: What is the equation of an ellipse with foci at (-6,-3),(0,-3) and a major axis of length 10? \n" ); document.write( "

Algebra.Com's Answer #699181 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "The center of the ellipse is at the point (-3,-3).\r\n" );
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document.write( "The major axis is horizontal line y= -3.\r\n" );
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document.write( "The major semi-axis is of the length a=  = 5.\r\n" );
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document.write( "The focal distance 2c is equal to  2c = 0 - (-6) = 6.\r\n" );
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document.write( "So, the eccentricity of the ellipse is 3: c = 3 = .\r\n" );
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document.write( "It implies 9 =  = ;  so,  b^2 = 25 - 9 = 16  and  b = 4.\r\n" );
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document.write( "Thus the minor semi-axis is b= 4.\r\n" );
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document.write( "Then the equation of the ellipse is\r\n" );
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document.write( " +  = 1,   or\r\n" );
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document.write( " +  = 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Your prerequisite is the lesson\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( "Your sample lessons are\r
\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( "    - General equation of an ellipse\r
\n" ); document.write( "\n" ); document.write( "    - Transform a general equation of an ellipse to the standard form by completing the square\r
\n" ); document.write( "\n" ); document.write( "    - Identify elements of an ellipse given by its general equation\r
\n" ); document.write( "\n" ); document.write( "in this site.\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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