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Equation of the transverse and conjugate axis of a hyperbola are respectively \( x+2 y-3=0 \), \( 2 x-y+4=0 \) and their respectively lengths are \( \sqrt{2} \) and \( \frac{2}{\sqrt{3}} \) then answer following :
\( \mathrm{P} \)
Coordinates of one of possible focus of hyperbola is
W
(A) \( \left(-1+\frac{2}{\sqrt{6}}, 2-\frac{1}{\sqrt{6}}\right) \)
(B) \( \left(\left(-1+\frac{2}{\sqrt{5}}\right),\left(2-\frac{1}{\sqrt{5}}\right)\right) \)
(C) \( \quad\left(\left(-1-\frac{2}{\sqrt{5}}\right),\left(2+\frac{1}{\sqrt{5}}\right)\right) \)
(D) \( \left(\left(-1-\frac{2}{\sqrt{5}}\right),\left(2-\frac{1}{\sqrt{5}}\right)\right) \)
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