If the line ax + by + c = 0 is a tangent to t | vedclass

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(B) Given the curve $xy = 4$,we can write $y = \frac{4}{x}$.Taking the derivative with respect to $x$,we get $\frac{dy}{dx} = -\frac{4}{x^2}$.The equa

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$a$ and $b$ have the same sign

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(B) Given the curve $xy = 4$,we can write $y = \frac{4}{x}$.Taking the derivative with respect to $x$,we get $\frac{dy}{dx} = -\frac{4}{x^2}$.The equation of the line is $ax + by + c = 0$,which can be rewritten as $y = -\frac{a}{b}x - \frac{c}{b}$.The slope of this line is $m = -\frac{a}{b}$.Since the line is a tangent to the curve,the slope of the tangent at any point $(x, y)$ on the curve must equal the slope of the line:$-\frac{4}{x^2} = -\frac{a}{b}$$\frac{4}{x^2} = \frac{a}{b}$.Since $x^2 > 0$ for all $x 
eq 0$ and $4 > 0$,it follows that $\frac{a}{b} > 0$.This implies that $a$ and $b$ must have the same sign (both positive or both negative).

If the line $ax + by + c = 0$ is a tangent to the curve $xy = 4$,then which of the following is true regarding the signs of $a$ and $b$?

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