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

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lamckee lamckee

02-01-2018
Mathematics

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

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Аноним Аноним · Answer 1 · 2018-01-02T19:16:37+01:00

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