document.write( "Question 1024307: find the center, foci and semi axes of the ellipse:
\n" ); document.write( "x^2+4y^2=4x+8y \n" ); document.write( "

Algebra.Com's Answer #640781 by fractalier(6550) $\"\"$ $\"About$

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Okay, let's rearrange
\n" ); document.write( "x^2+4y^2=4x+8y to get
\n" ); document.write( "x^2 - 4x + 4y^2 - 8y = 0
\n" ); document.write( "x^2 - 4x + 4 + 4(y^2 - 2y + 1) = 4 + 4
\n" ); document.write( "(x-2)^2 + 4(y-1)^2 = 8
\n" ); document.write( "Now divide by 8
\n" ); document.write( " $\"%28x-2%29%5E2%2F8+%2B+%28y-1%29%5E2%2F2+=+1\"$
\n" ); document.write( "The center is (2,1).
\n" ); document.write( "The semi-major axes are 2*sqrt(2).
\n" ); document.write( "The semi-minor axes are sqrt(2).
\n" ); document.write( "The focal distance is found via c^2 = a^2 - b^2 = 6.
\n" ); document.write( "Thus the foci are sqrt(6) to the left and right of the center (2,1). \n" ); document.write( "

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