If the straight line (a-1)x - by + 4 = 0 is n | vedclass

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(B) The equation of the line is $(a-1)x - by + 4 = 0$. Its slope is $m = \frac{a-1}{b}$. The hyperbola is $xy = 1$, so $y = \frac{1}{x}$. The derivati

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$a > 1, b < 0$

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(B) The equation of the line is $(a-1)x - by + 4 = 0$. Its slope is $m = \frac{a-1}{b}$. The hyperbola is $xy = 1$, so $y = \frac{1}{x}$. The derivative is $\frac{dy}{dx} = -\frac{1}{x^2}$. The slope of the tangent at point $(x_0, y_0)$ is $-\frac{1}{x_0^2}$. The slope of the normal is $x_0^2$, which is always positive $(x_0^2 > 0)$. Thus, $\frac{a-1}{b} > 0$. This inequality holds if $(a-1 > 0 	ext{ and } b > 0)$ or $(a-1 This simplifies to $(a > 1, b > 0)$ or $(a Therefore, the conditions $a > 1, b  0$ do not hold.

If the straight line $(a-1)x - by + 4 = 0$ is normal to the hyperbola $xy = 1$, then which of the following does not hold?

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