document.write( "Question 214701: what is the lenght of the major axis of the ellipse 3x(2power)+4y(2power)=12? \n" ); document.write( "

Algebra.Com's Answer #162145 by Earlsdon(6294) $\"\"$ $\"About$

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Given the equation for an ellipse, find the length of the major axis:
\n" ); document.write( " $\"3x%5E2%2B4y%5E2+=+12\"$ Re-arrange this to the standard form of the equation of an ellipse with major axis on the x-axis: $\"%28x%5E2%2Fa%5E2%29%2B%28y%5E2%2Fb%5E2%29+=+1\"$ where a = the semi-major axis and b = the semi-minor axis.
\n" ); document.write( " $\"3x%5E2%2B4y%5E2+=+12\"$ Divide both sides by 12.
\n" ); document.write( " $\"%283x%5E2%2F12%29%2B%284y%5E2%2F12%29+=+1\"$ Simplify the left side.
\n" ); document.write( " $\"%28x%5E2%2F4%29%2B%28y%5E2%2F3%29+=+1\"$ Compare with the standard form:
\n" ); document.write( " $\"%28x%5E2%2Fa%5E2%29%2B%28y%5E2%2Fb%5E2%29+=+1\"$
\n" ); document.write( " $\"a%5E2+=+4\"$ Take the square root of both sides.
\n" ); document.write( " $\"a+=+2\"$ This is the length of the semi-major axis.
\n" ); document.write( " $\"2a+=+4\"$ This is the length of the major axis.
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