document.write( "Question 259707: Given the ellipse: 2x^2 + 6y^2 + 32x - 48y + 212 = 0 find.
\n" ); document.write( "a. The Center C
\n" ); document.write( "b. Length of Major Axis
\n" ); document.write( "c. Length of Minor Axis
\n" ); document.write( "d. Distance from C to foci \n" ); document.write( "

Algebra.Com's Answer #191157 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
We have this original equation as
\n" ); document.write( "(i) $\"2x%5E2+%2B+6y%5E2+%2B+32x+-+48y+%2B+212+=+0\"$
\n" ); document.write( "rearranging, we get
\n" ); document.write( "(ii) $\"%282x%5E2+%2B+32x%29+%2B+%286y%5E2+-+48y%29+=+-212\"$
\n" ); document.write( "complete the square to get
\n" ); document.write( "(iii) $\"2%28x%2B8%29%5E2+%2B+6%28y-4%29%5E2+=+-212+%2B+128+%2B96\"$
\n" ); document.write( "to get
\n" ); document.write( "(iv) $\"2%28x%2B8%29%5E2+%2B+6%28y-4%29%5E2+=+12\"$
\n" ); document.write( "dividing by 12, we get
\n" ); document.write( "(v) $\"%28%28x%2B8%29%5E2%29%2F6+%2B+%28%28y-4%29%5E2%29%2F2+=+1\"$
\n" ); document.write( "---
\n" ); document.write( "center is (-8,4)
\n" ); document.write( "--
\n" ); document.write( "major axis = sqrt(6)
\n" ); document.write( "--
\n" ); document.write( "minor axis = sqrt(2)
\n" ); document.write( "--
\n" ); document.write( "distance to foci
\n" ); document.write( "sqrt(sqrt(6) - sqrt(2)) = sqrt(4) = 2 \n" ); document.write( "

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