SOLUTION: Determine the standard equation of the hyperbola whose general equation is 5x^2-4y^2-20x-24y-36=0.

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Question 1186522: Determine the standard equation of the hyperbola whose general equation is 5x^2-4y^2-20x-24y-36=0.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


5x%5E2-4y%5E2-20x-24y-36=0

(1) group the x and y terms together; factor out the leading coefficients for both variables; move the constant to the other side:
5%28x%5E2-4x%29-4%28y%5E2%2B6y%29=36

(2) complete the square in x and y, making sure to add/subtract appropriate constants on the right to keep the equation balanced:
5%28x%5E2-4x%2B4%29-4%28y%5E2%2B6y%2B9%29=36%2B20-36=20

(3) divide by the constant on the right (to make the right side equal to 1); write the expression for each variable as a binomial square:
%28x-2%29%5E2%2F4-%28y%2B3%29%5E2%2F5=1

Done....