Question

. If the line ax +by+c=0 is a tangent to the curve xy=4, then the possible answer is (a) a > 0, b>0 (b) a>0, b< 0 (c) a<0, b>0 (d) none of these

JEE/Engineering Exams

Maths

Solution

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[ x y=4 quad Rightarrow quad y=frac{4}{x} ] ( frac{d y}{d x}=frac{-4}{x^{2}}= ) slope of tangeut ( =frac{-a}{b} ) ( begin{aligned} Rightarrow quad x^{2}=frac{4 b}{a} Rightarrow frac{b}{a}>0 Rightarrow & b>0, a>0 end{aligned} ) or ( b<0, a<0 ) Option ( (a) ) is corred