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White raven [17]
3 years ago
9

What is the hyperbola 25x^2-100y-9y^2-90x-350=0 in standard form?

Mathematics
1 answer:
sergij07 [2.7K]3 years ago
4 0
WE need to complete the square on the x and y terms:-

25x^2 - 100x - 9y^2 - 90y = 350
25(x^2 - 4x +    ) - 9(y^2 + 10x       )  =   350 + 25(  )  - 9(  )
25(x^2 - 4x  + 4 ) - 9(y^2 + 10x  + 25)  = 350  + 25(4)  - 9(25)
25(x - 2)^2 - 9(y + 5)^2 = 

25(x - 2)^2   -  9(y + 5)^2          =  225
----------------    --------------            --------
    225                 225                    225

  ( x  - 2)^2         (y + 5)^2  
  -------------   -   --------------  =    1         Answer
        9                    25                               



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