The equations of the transverse and conjugate axes of a hyperbola a...

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The equations of the transverse and conjugate axes of a hyperbola are respectively \( x+2 y-3=0 \),
\( \mathrm{P} \) \( 2 x-y+4=0 \), and their respective lengths are \( \sqrt{2} \) and \( 21 \sqrt{3} \). Then find the equation of the hyperbola.

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