If the foci of a hyperbola lie on \( y=x \) and one of the asymptotes is \( y=2 x \), then the e...

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If the foci of a hyperbola lie on \( y=x \) and one of the asymptotes is \( y=2 x \), then the equation of the hyperbola, given that it passes through \( (3,4) \), is:
(a) \( \mathrm{x}^{2}-\mathrm{y}^{2}-\frac{5}{2} \mathrm{xy}+5=0 \)
(b) \( 2 x^{2}-2 y^{2}+5 x y+5=0 \)
(c) \( 2 x^{2}+2 y^{2}-5 x y+10=0 \)
(d) None of these
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