SOLUTION: Reduce into standard equation of the hyperbola. 25x²-50x-9y²-36y-236=0

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Question 1187587: Reduce into standard equation of the hyperbola. 25x²-50x-9y²-36y-236=0
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The standard form is

%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1

Or there is the possibility that it will turn out to be

%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1

Given:
25x%5E2-50x-9y%5E2-36y-236+=+0

(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:
%2825x%5E2-50x%29-%289y%5E2%2B36y%29+=+236
25%28x%5E2-2x%29-9%28y%5E2%2B4y%29+=+236
25%28x%5E2-2x%2B1%29-9%28y%5E2%2B4y%2B4%29+=+236%2B25-36
25%28x-1%29%5E2-9%28y%2B2%29%5E2=225

(2) Divide by the constant:
%28x-1%29%5E2%2F9-%28y%2B2%29%5E2%2F25=1