document.write( "Question 884823: Convert the equation to the standard form for a hyperbola by completing the square on x and y. \r
\n" ); document.write( "\n" ); document.write( "y2 - 25x2 + 4y + 50x - 46 = 0 \n" ); document.write( "

Algebra.Com's Answer #534774 by KMST(5328) $\"\"$ $\"About$

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$\"y%5E2-25x%5E2%2B4y%2B50x-46=0\"$
\n" ); document.write( " $\"y%5E2-25x%5E2%2B4y%2B50x=46\"$
\n" ); document.write( " $\"y%5E2%2B4y-25x%5E2%2B50x=46\"$
\n" ); document.write( "Recognizing that $\"y%5E2%2B4y\"$ is part of =(y+2)^2}}} ,
\n" ); document.write( "we add $\"4\"$ to both sides of the equal sign to complete one square on the left side:
\n" ); document.write( " $\"y%5E2%2B4y%2B4-25x%5E2%2B50x=46%2B4\"$
\n" ); document.write( "Replacing $\"%28y%2B2%29%5E2\"$ for $\"y%5E2%2B4y%2B4\"$ (on the left of the equal sign),
\n" ); document.write( "taking out $\"%28-25%29\"$ as a common factor (also on the left),
\n" ); document.write( "and just performing indicated operations on the right side:
\n" ); document.write( " $\"%28y%2B2%29%5E2-25%28x%5E2-2x%29=50\"$
\n" ); document.write( "Recognizing that $\"x%5E2-2x\"$ is part of $\"x%5E2-2x%2B1=%28x-1%29%5E2\"$ ,
\n" ); document.write( "we add $\"%28-25%29%2A1=-25\"$ to both sides of the equation to complete another square:
\n" ); document.write( " $\"%28y%2B2%29%5E2-25%28x%5E2-2x%29-25%2A1=50-25\"$
\n" ); document.write( " $\"%28y%2B2%29%5E2-25%28x%5E2-2x%2B1%29=25\"$
\n" ); document.write( " $\"%28y%2B2%29%5E2-25%28x-1%29%5E2=25\"$
\n" ); document.write( "Dividing both sides by $\"25=5%5E2\"$ we get:
\n" ); document.write( " $\"%28y%2B2%29%5E2%2F25-25%28x-1%29%5E2%2F25=25%2F25\"$
\n" ); document.write( " $\"%28y%2B2%29%5E2%2F25-%28x-1%29%5E2%2F1=1\"$
\n" ); document.write( " $\"%28y%2B2%29%5E2%2F5%5E2-%28x-1%29%5E2%2F1%5E2=1\"$ \n" ); document.write( "

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