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If the line ax+by+c=0 is a normal to the curve xy=1 then

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a<0, b<0

a>0, b<0 (or) a<0, b>0

None of these

a>0, b>0

answer is B.

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Detailed Solution

$xy = 1 \Rightarrow y = \frac{1}{x} \Rightarrow \frac{dy}{dx} = \frac{- 1}{x^{2}}$
$\Rightarrow$ slope of normal = x²
$∴ x^{2} = - \frac{a}{b}$
Clearly a<0, b>0 (or) a>0, b<0

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