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The equations of the transverse and conjugate axes
\( \mathrm{P}^{12: 3} \) of a hyperbola are, respectively, \( x+2 y-3=0 \) and

W \( 2 x-y+4=0 \), and their respective lengths are \( \sqrt{2} \) and \( \frac{2}{\sqrt{3}} \). The equation of the hyperbola is
(1) \( 2 / 5(x+2 y-3)^{2}-3 / 5(2 x-y+4)^{2}=1 \)
(2) \( 2 / 5(2 x-y+4)^{2}-3 / 5(x+2 y-3)^{2}=1 \)
(3) \( 2(2 x-y+4)^{2}-3(x+2 y-3)^{2}=1 \)
(4) \( 2(x+2 y-3)^{2}-3(2 x-y+4)^{2}=1 \)
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