SOLUTION: Convert the equation to the standard form for a hyperbola by completing the square on x and y. y2 - 25x2 + 4y + 50x - 46 = 0

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Question 884823: Convert the equation to the standard form for a hyperbola by completing the square on x and y.
y2 - 25x2 + 4y + 50x - 46 = 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-25x%5E2%2B4y%2B50x-46=0
y%5E2-25x%5E2%2B4y%2B50x=46
y%5E2%2B4y-25x%5E2%2B50x=46
Recognizing that y%5E2%2B4y is part of =(y+2)^2}}} ,
we add 4 to both sides of the equal sign to complete one square on the left side:
y%5E2%2B4y%2B4-25x%5E2%2B50x=46%2B4
Replacing %28y%2B2%29%5E2 for y%5E2%2B4y%2B4 (on the left of the equal sign),
taking out %28-25%29 as a common factor (also on the left),
and just performing indicated operations on the right side:
%28y%2B2%29%5E2-25%28x%5E2-2x%29=50
Recognizing that x%5E2-2x is part of x%5E2-2x%2B1=%28x-1%29%5E2 ,
we add %28-25%29%2A1=-25 to both sides of the equation to complete another square:
%28y%2B2%29%5E2-25%28x%5E2-2x%29-25%2A1=50-25
%28y%2B2%29%5E2-25%28x%5E2-2x%2B1%29=25
%28y%2B2%29%5E2-25%28x-1%29%5E2=25
Dividing both sides by 25=5%5E2 we get:
%28y%2B2%29%5E2%2F25-25%28x-1%29%5E2%2F25=25%2F25
%28y%2B2%29%5E2%2F25-%28x-1%29%5E2%2F1=1
%28y%2B2%29%5E2%2F5%5E2-%28x-1%29%5E2%2F1%5E2=1