document.write( "Question 1043225: Find the center,foci,vertices and covertices of the ellipse with the given equation.\r
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Algebra.Com's Answer #658349 by ikleyn(52794)\"\" \"About 
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document.write( "\"9x%5E2%2B16y%5E2-126x%2B64y\" = \"71\"  --->\r\n" );
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document.write( "\"9%2A%28x%5E2-14x%29+%2B+16%2A%28y%5E2%2B4y%29\" = \"71\"  --->\r\n" );
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document.write( "\"9%2A%28x-7%29%5E2+-+9%2A49+%2B+16%2A%28y%2B2%29%5E2+-+16%2A4\" = \"171\",\r\n" );
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document.write( "\"9%2A%28x-7%29%5E2+%2B+16%2A%28y%2B2%29%5E2\" = \"171%2B9%2A49+%2B+16%2A4\",\r\n" );
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document.write( "\"9%2A%28x-7%29%5E2+%2B+16%2A%28y%2B2%29%5E2\" = \"171%2B9%2A49+%2B+16%2A4\",\r\n" );
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document.write( "\"9%2A%28x-7%29%5E2+%2B+16%2A%28y%2B2%29%5E2\" = \"676\",      ( <--- next divide both sides by 676 = \"26%5E2\" )\r\n" );
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document.write( "\"%28x-7%29%5E2%2F%2826%2F3%29%5E2+%2B+%28y%2B2%29%5E2%2F%2826%2F4%29%5E2\" = 1,  or\r\n" );
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document.write( "\"%28x-7%29%5E2%2F%2826%2F3%29%5E2+%2B+%28y%2B2%29%5E2%2F%2813%2F2%29%5E2\" = 1.\r\n" );
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document.write( "The center of the ellipse is the point  (7,-2).\r\n" );
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document.write( "The semi-major axis is a = \"26%2F3\".\r\n" );
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document.write( "The semi-minor axis is b = \"26%2F4\" = 13/2.   (Notice that a > b. The major axis is horizontal, and the ellipse is wider than tall).\r\n" );
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document.write( "Two vertices in horizontal directions are  (\"7%2B%2826%2F3%29\",\"-2\")  and  (\"7-%2826%2F3%29\",\"-2\").\r\n" );
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document.write( "Two vertices in vertical directions are  (\"7\",\"-2%2B%2813%2F2%29\")  and  (\"7\",\"-2-%2813%2F2%29\").\r\n" );
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document.write( "The linear eccentricity is c = \"sqrt%28a%5E2-b%5E2%29\" = \"sqrt%28%2826%2F3%29%5E2-%2826%2F4%29%5E2%29\" = \"26%2Asqrt%28%281%2F9%29-%281%2F16%29%29\" = \"26%2Asqrt%28%2816-9%29%2F%289%2A16%29%29\" = \"%2826%2F%283%2A4%29%29%2Asqrt%287%29\" = \"%2813%2F6%29%2Asqrt%287%29\".\r\n" );
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document.write( "The foci are  (\"7%2B%2813%2F6%29sqrt%287%29\",\"-2\")  and  (\"7-%2813%2F6%29sqrt%287%29\",\"-2\").\r\n" );
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