document.write( "Question 39142: Locate the foci with this equation:\r
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\n" ); document.write( "*= squared. (EX: 5squared) \n" ); document.write( "
Algebra.Com's Answer #24575 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Locate the foci with this equation:\r\n" );
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document.write( "(x - 5)²    (y - 3)²\r\n" );
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document.write( "   5²         10²\r\n" );
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document.write( "There are two forms of ellipses.\r\n" );
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document.write( "1. Those that are longer horizontally and narrower vertically\r\n" );
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document.write( "These have the form:\r\n" );
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document.write( "(x - h)²   (y - k)²\r\n" );
document.write( "———————— + ———————— = 1\r\n" );
document.write( "   a²         b²\r\n" );
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document.write( "a = semi-major axis, b = semi-minor axis, (h, k) = center\r\n" );
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document.write( "center = (h, k)\r\n" );
document.write( "vertices = (h±a, k)        _______\r\n" );
document.write( "foci = (h±c, k) where c = Öa² - b² \r\n" );
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document.write( "2. Those that are longer vertically and narrower horizontally\r\n" );
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document.write( "(x - h)²   (y - k)²\r\n" );
document.write( "———————— + ———————— = 1\r\n" );
document.write( "   b²         a²\r\n" );
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document.write( "a = semi-major axis, b = semi-minor axis, (h, k) = center\r\n" );
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document.write( "center = (h, k)\r\n" );
document.write( "vertices = (h, k±a)        _______\r\n" );
document.write( "foci = (h, k±c) where c = Öa² - b² \r\n" );
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document.write( "You can always tell which type ellipse you have because\r\n" );
document.write( "the semi major axis a is always greater than the semi minor\r\n" );
document.write( "axis b.  Therefore a² will always be larger than b².  If\r\n" );
document.write( "a² is under the (x-h)², the ellipse is the first type. Otherwise\r\n" );
document.write( "it is the second type.\r\n" );
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document.write( "Yours is the second type because the larger of 5² and 10² is\r\n" );
document.write( "10² and it is underneath (y-k)².\r\n" );
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document.write( "a = 10\r\n" );
document.write( "b = 5\r\n" );
document.write( "center = (h, k) = (5. 3)\r\n" );
document.write( "vertices = (h, k±a) = (5, 3±10), that is, (5, -7) and (5, 13) \r\n" );
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document.write( "To find the foci, we need to find c\r\n" );
document.write( "     _______\r\n" );
document.write( "c = Öa² - b² \r\n" );
document.write( "     ________\r\n" );
document.write( "c = Ö10² - 5² \r\n" );
document.write( "     ________\r\n" );
document.write( "c = Ö100 - 25\r\n" );
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document.write( "c = Ö75\r\n" );
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document.write( "c = Ö25·3\r\n" );
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document.write( "c = 5Ö3\r\n" );
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document.write( "foci = (h, k±c) = (5, 3±5Ö3), that is\r\n" );
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document.write( "(5, 3-5Ö3) and (5, 3+5Ö3)\r\n" );
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document.write( "Your ellipse looks like this:\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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