document.write( "Question 1185816: Center at (2,-2) vertex at (7,-2) and focus (4,-2) find the equation of the ellipse \n" ); document.write( "
Algebra.Com's Answer #816658 by ikleyn(52805)\"\" \"About 
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\n" ); document.write( "Center at (2,-2) vertex at (7,-2) and focus (4,-2) find the equation of the ellipse
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document.write( "(1)  Notice that the center and the vertex (and the focus) all lie on horizontal line y = -2.\r\n" );
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document.write( "     It means that the major axis is horizontal, and the major semi-axis is horizontal, too.\r\n" );
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document.write( "     \r\n" );
document.write( "(2)  The length of the major semi-axis  \" a \"  is the distance between the vertex and the center, \r\n" );
document.write( "     i.e. equals 7-2 = 5 units:  a = 5.\r\n" );
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document.write( "(3)  The focal distance (between the center and the focus) is  4-2 = 2 units:  c = 2.\r\n" );
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document.write( "     Hence, for the minor semi-axis  \"b\"  we have  b = \"sqrt%285%5E2+%2B+2%5E2%29\" = \"sqrt%2829%29\".\r\n" );
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document.write( "(4) Thus the standard form equation of the ellipse is \r\n" );
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document.write( "         \"%28x-2%29%5E2%2F5%5E2\" + \"%28y-%28-2%29%29%5E2%2F29\" = 1,\r\n" );
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document.write( "     or\r\n" );
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document.write( "         \"%28x-2%29%5E2%2F25\" + \"%28y%2B2%29%5E2%2F29\" = 1.      ANSWER\r\n" );
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