document.write( "Question 269783: How do I write the equation of the ellipse $\"9x%5E2+%2B+4y%5E2+-+36x+%2B+24y+%2B+36+=+0\"$ in standard form? Thank-you! \n" ); document.write( "

Algebra.Com's Answer #197762 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
Here is our equation
\n" ); document.write( " $\"9x%5E2+%2B+4y%5E2+-+36x+%2B+24y+%2B+36+=+0\"$
\n" ); document.write( "step 1 - rearrange so that x's are together and y's are together as
\n" ); document.write( " $\"9x%5E2+-+36x+%2B+4y%5E2+%2B+24y+%2B+36+=+0\"$
\n" ); document.write( "step 2 - complete the square on both x's and y's to get
\n" ); document.write( " $\"9%28x%5E2+-+4x+%2B+______%29+%2B+4%28y%5E2+%2B+6y+%2B+_____%29+=+-36+%2B+_____+%2B+______\"$
\n" ); document.write( "The blanks are waiting for numbers . . .
\n" ); document.write( "step 3 - take (1/2) middle term and square it. PUt these into the left side of blanks as
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\n" ); document.write( "we added 4 into the x's, but there is a 9 in front, so we really added 36. add 36 to the right side to keep it balanced.
\n" ); document.write( "we added 9 into the y's, but there is a 4 in front, so we really added 36. add another 36 to the right side to keep it balanced. we get
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\n" ); document.write( "step 4 - rewrite the left side as 2 binomials squared and simplify the right side as
\n" ); document.write( " $\"9%28x-2%29%5E2+%2B+4%28y%2B3%29%5E2+=+36\"$
\n" ); document.write( "step 5 - divide by 36 to get
\n" ); document.write( " $\"%28x-2%29%5E2%2F4+%2B+%28y%2B3%29%5E2%2F9+=+1\"$ \n" ); document.write( "

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