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The center of the hyperbola $4 (2 y - x - 3)^{2} - 9 (2 x + y - 1)^{2} = 80$

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$(- \frac{1}{5}, \frac{7}{5})$

$(- \frac{2}{5}, \frac{13}{10})$

none of these

$(1, 2)$

answer is B.

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Detailed Solution

The equation of the hyperbola is

$4 (2 y - x - 3)^{2} - 9 (2 x + y - 1)^{2} = 80$

The center of the hyperbola is obtained from the equations

$2 y - x - 3 = 0 and 2 x + y - 1 = 0$

Solving, we get,

$and \begin{array}{l} x = - 1 / 5 \\ y = 7 / 5 \end{array}$

Hence, the center is $(- \frac{1}{5}, \frac{7}{5})$

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