document.write( "Question 1144228: Determine the general equation of the ellipse with center (0,0), a focus of (0, √7), and a vertex of (0,4). \n" ); document.write( "

Algebra.Com's Answer #765280 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The post by @greenestamps has some typos.\r
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document.write( "The center is at (0,0), and the coordinates of the vertex and focus tell us the major axis is vertical.  \r\n" );
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document.write( "It means that the ellipse is TALLER than WIDE. The general equation is then\r\n" );
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document.write( " +  = 1        (1)\r\n" );
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document.write( "where a is the semi-major axis and b is the semi-minor axis.\r\n" );
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document.write( "Notice that the major semi-axis \"a\" is associated with y-term in equation (1): it is because the ellipse is TALLER than WIDE.\r\n" );
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document.write( "The distance from the center to each focus is c, where a, b, and c are related by\r\n" );
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document.write( " =  -       (2)        ( <<<---=== it is the line where I fixed the typo (!) )\r\n" );
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document.write( "The given coordinates of a focus and a vertex tell us c = sqrt(7) and a = 4.\r\n" );
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document.write( "Therefore,   =  -  =  -  = 16 - 7 = 9   and  b =  = 3.\r\n" );
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document.write( "Thus the final equation of this ellipse is\r\n" );
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document.write( "     +  = 1,\r\n" );
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document.write( "or\r\n" );
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document.write( "     +  = 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This reference might be useful to you\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( "It is my lesson in this site, which contains all relevant formulas related to ellipses.\r
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