document.write( "Question 307600: I need to write the following in standard form can you help me?
\n" ); document.write( "X^2+9y^2-4X+54Y+49=0 thank you so much
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Algebra.Com's Answer #220047 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Write in standard form:
\n" ); document.write( " $\"x%5E2%2B9y%5E2-4x%2B54y%2B49+=+0\"$ Group like-terms together:
\n" ); document.write( " $\"%28x%5E2-4x%29%2B%289y%5E2%2B54y%29%2B49+=+0\"$ Subtract 49 from both sides.
\n" ); document.write( " $\"%28x%5E2-4x%29%2B%289y2%2B54y%29+=+-49\"$ Factor out a 9 from the second group.
\n" ); document.write( " $\"%28x%5E2-4x%29%2B9%28y%5E2%2B6y%29+=+-49\"$ Now complete the squares in x and y.
\n" ); document.write( " $\"%28x%5E2-4x%2B4%29%2B9%28y%5E2%2B6y%2B9%29+=+-49%2B4%2B81\"$ Factor the left side and simplify the right side.
\n" ); document.write( " $\"%28x-2%29%5E2%2B9%28y%2B3%29%5E2+=+36\"$ Now divide through by 36.
\n" ); document.write( " $\"%28x-2%29%5E2%2F36+%2B+%28y%2B3%29%5E2%2F4+=+1\"$ Rewrite as:
\n" ); document.write( " $\"highlight%28%28x-2%29%5E2%2F6%5E2+%2B+%28y%2B3%29%5E2%2F2%5E2+=+1%29\"$
\n" ); document.write( "You may recognize this as the equation of an ellipse, in standard form, whose major axis is parallel to the x-axis, with its center at (2, -3), its semi-major axis = 6 and its semi-minor axis = 2.
\n" ); document.write( "The standard form of the equation of an ellipse with its major axis parallel to the x-axis, center at (h, k), and $\"a%5E2+%3E+b%5E2\"$ looks like:
\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2+=+1\"$ \n" ); document.write( "

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