The equations of the transverse and conjugate axis of a hyperbola are, respectively, \( x+2 y-3=...

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The equations of the transverse and conjugate axis of a hyperbola are, respectively, \( x+2 y-3=0 \) and \( 2 x-y+4=0 \), and their respective lengths are \( \sqrt{2} \) and \( \frac{2}{\sqrt{3}} \)
The equation of the hyperbola is:
(a) \( \frac{2}{5}(x+2 y-3)^{2}-\frac{3}{5}(2 x-y+4)^{2}=1 \)
(b) \( \frac{2}{5}(2 x-y+4)^{2}-\frac{3}{5}(x+2 y-3)^{2}=1 \)
(c) \( 2(2 x-y+4)^{2}-3(x+2 y-3)^{2}=1 \)
(d) \( 2(x+2 y-3)^{2}-3(2 x-y+4)^{2}=1 \)
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