document.write( "Question 979639: find an equation of the ellipse having a major axis of length 12 and foci at (1,2) and (-3,2) \n" ); document.write( "
Algebra.Com's Answer #600945 by Edwin McCravy(20056)\"\" \"About 
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find an equation of the ellipse having a major axis of length 12 and foci at
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We plot the foci (1,2) and (-3,2). \r\n" );
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document.write( "Then we plot the center which is the midpoint between the two foci,\r\n" );
document.write( "which is (-1,2). Then we draw the major axis 12 units long,\r\n" );
document.write( "with the center at the middle, which means that we draw it 6 units \r\n" );
document.write( "on each side of the focus (in green).  That means that the vertices are \r\n" );
document.write( "(-7,2) and (5,2). \r\n" );
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document.write( "We know that this ellipse looks like this:\"drawing%2820%2C10%2C-2%2C2%2C-1%2C1%2Carc%280%2C0%2C-3.9%2C1.9%29+%29\".\r\n" );
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document.write( "Therefore its equation is \r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "The center is (h,k) = (-1,2).\r\n" );
document.write( "We know that \"a\" = half the major axis = half of 12 = 6\r\n" );
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document.write( "So we can fill in h,k, and a:\r\n" );
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document.write( "\"%28x%2B1%29%5E2%2F6%5E2%2B%28y-2%29%5E2%2Fb%5E2=1\"\r\n" );
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document.write( "\"%28x%2B1%29%5E2%2F36%2B%28y-2%29%5E2%2Fb%5E2=1\"\r\n" );
document.write( "We only need b, the semi-minor axis:\r\n" );
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document.write( "We calculate b from \"c%5E2=a%5E2-b%5E2\"\r\n" );
document.write( "                    \"2%5E2=6%5E2-b%5E2\"\r\n" );
document.write( "                    \"4=36-b%5E2\"\r\n" );
document.write( "                    \"b%5E2=32\"\r\n" );
document.write( "                    \"b=sqrt%2832%29\"\r\n" );
document.write( "                    \"b=sqrt%2816%2A2%29\"\r\n" );
document.write( "                    \"b=4sqrt%282%29\", approximately 5.7 units\r\n" );
document.write( "                    up and down from the center. \r\n" );
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document.write( "So the equation is \r\n" );
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document.write( "\"%28x%2B1%29%5E2%2F36%2B%28y-2%29%5E2%2F32=1\"  \r\n" );
document.write( "                   \r\n" );
document.write( "It looks like a circle but I'll draw a circle (in red) so you\r\n" );
document.write( "can see that it's not quite a circle:\r\n" );
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document.write( "Edwin
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