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(B) The equation of the hyperbola is $14 x^2+38 x y+20 y^2+x-7 y-91=0$. Asymptotes of a hyperbola differ from the hyperbola equation by a constant. Le

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$2 x+4 y+1=0$

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(B) The equation of the hyperbola is $14 x^2+38 x y+20 y^2+x-7 y-91=0$. Asymptotes of a hyperbola differ from the hyperbola equation by a constant. Let the asymptotes be $(7 x+5 y+c_1)(2 x+4 y+c_2) = 14 x^2+38 x y+20 y^2+x-7 y+k = 0$. Expanding the product: $14 x^2+28 x y+7 x c_2+10 x y+20 y^2+5 y c_2+2 x c_1+4 y c_1+c_1 c_2 = 14 x^2+38 x y+20 y^2+x(7 c_2+2 c_1)+y(5 c_2+4 c_1)+c_1 c_2$. Comparing the coefficients with the given hyperbola equation: $7 c_2+2 c_1 = 1$ $5 c_2+4 c_1 = -7$ Given one asymptote is $7 x+5 y-3=0$,so $c_1 = -3$. Substituting $c_1 = -3$ in the first equation: $7 c_2 + 2(-3) = 1$ $\Rightarrow 7 c_2 - 6 = 1$ $\Rightarrow 7 c_2 = 7$ $\Rightarrow c_2 = 1$. Thus,the other asymptote is $2 x+4 y+1=0$.

If the equation of one asymptote of the hyperbola $14 x^2+38 x y+20 y^2+x-7 y-91=0$ is $7 x+5 y-3=0$,then the other asymptote is

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