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(B) Given,the centre is $(0, 0)$,the foci are $(\pm 3, 0)$,and the eccentricity $e = \frac{3}{2}$.Since the foci are $(\pm ae, 0) = (\pm 3, 0)$,we hav

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does not intersect the hyperbola

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(B) Given,the centre is $(0, 0)$,the foci are $(\pm 3, 0)$,and the eccentricity $e = \frac{3}{2}$.Since the foci are $(\pm ae, 0) = (\pm 3, 0)$,we have $ae = 3$.Substituting $e = \frac{3}{2}$,we get $a(\frac{3}{2}) = 3$,which implies $a = 2$.Using the relation $b^2 = a^2(e^2 - 1)$,we have $b^2 = 2^2((\frac{3}{2})^2 - 1) = 4(\frac{9}{4} - 1) = 4(\frac{5}{4}) = 5$.The equation of the hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,which is $\frac{x^2}{4} - \frac{y^2}{5} = 1$,or $5x^2 - 4y^2 = 20$.To check the intersection with the line $y = 2x - 1$,substitute $y$ into the hyperbola equation:$5x^2 - 4(2x - 1)^2 = 20$$5x^2 - 4(4x^2 - 4x + 1) = 20$$5x^2 - 16x^2 + 16x - 4 = 20$$-11x^2 + 16x - 24 = 0$$11x^2 - 16x + 24 = 0$.The discriminant $D = b^2 - 4ac = (-16)^2 - 4(11)(24) = 256 - 1056 = -800$.Since $D < 0$,the line does not intersect the hyperbola.

Let the origin be the centre,$(\pm 3, 0)$ be the foci,and $\frac{3}{2}$ be the eccentricity of a hyperbola. Then the line $2x - y - 1 = 0$

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