document.write( "Question 1187587: Reduce into standard equation of the hyperbola. 25x²-50x-9y²-36y-236=0 \n" ); document.write( "

Algebra.Com's Answer #818616 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The standard form is

\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$

\n" ); document.write( "Or there is the possibility that it will turn out to be

\n" ); document.write( " $\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"$

\n" ); document.write( "Given:
\n" ); document.write( " $\"25x%5E2-50x-9y%5E2-36y-236+=+0\"$

\n" ); document.write( "(1) Move the constant to the other side and complete the square in x and y, remembering to keep the equation balanced by adding the same quantities to both sides:
\n" ); document.write( " $\"%2825x%5E2-50x%29-%289y%5E2%2B36y%29+=+236\"$
\n" ); document.write( " $\"25%28x%5E2-2x%29-9%28y%5E2%2B4y%29+=+236\"$
\n" ); document.write( " $\"25%28x%5E2-2x%2B1%29-9%28y%5E2%2B4y%2B4%29+=+236%2B25-36\"$
\n" ); document.write( " $\"25%28x-1%29%5E2-9%28y%2B2%29%5E2=225\"$

\n" ); document.write( "(2) Divide by the constant:
\n" ); document.write( " $\"%28x-1%29%5E2%2F9-%28y%2B2%29%5E2%2F25=1\"$

\n" ); document.write( " \n" ); document.write( "

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