A) \[a>0,b>0\]
B) \[a>0,b<0\]
C) \[a<0,b<0\]
D) Data is insufficient
Correct Answer: B
Solution :
The given equation of curve is \[xy=1\] On differentiating with respect to x, we get \[x\frac{dy}{dx}+y=0\Rightarrow \frac{dy}{dx}=-\frac{y}{x}\] This is the slope of the tangent to the curve \[xy=1\] Let \[\left( t,\frac{1}{t} \right)\] be any point on the curve at which normal to the curve can be drawn. \[\therefore \,\,{{\left( \frac{dy}{dx} \right)}_{\left( t,\frac{1}{t} \right)}}=-\frac{1}{{{t}^{2}}}\] So, slope of normal \[={{t}^{2}}\] Therefore the given line \[ax+by+c=0\]will be normal to the curve if \[{{t}^{2}}=\frac{-b}{a}\] since \[{{t}^{2}}>0\Rightarrow \frac{-b}{a}>0\] \[\Rightarrow \] either \[b>0,a<0\] or \[a>0,b<0\]
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