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If the line $a x+b y+c=0$ is a tangent to the curve $x y=4$, then
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2913 Upvotes
Verified Answer
The correct answer is:
a $ < 0$, b $ < 0$
$$
\begin{aligned}
& \text { Hints: Slope of line }=-\frac{a}{b} \\
& y=\frac{4}{x}=1, \frac{d y}{d x}=-\frac{4}{x^2},-\frac{a}{b}=-\frac{4}{x^2} \Rightarrow \frac{a}{b}=\frac{4}{x^2}>0 \\
& a < 0, b < 0
\end{aligned}
$$
\begin{aligned}
& \text { Hints: Slope of line }=-\frac{a}{b} \\
& y=\frac{4}{x}=1, \frac{d y}{d x}=-\frac{4}{x^2},-\frac{a}{b}=-\frac{4}{x^2} \Rightarrow \frac{a}{b}=\frac{4}{x^2}>0 \\
& a < 0, b < 0
\end{aligned}
$$
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