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If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other, then the points $P(x, y)$ on such lines satisfy
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Verified Answer
The correct answer is:
$4 x y < 1$
Equation of line is moving such that intercept mode by it on the coordinate axis are reciprocal to each other is
$a x+\frac{y}{a}=1 \Rightarrow a^2 x-a+y=0$
$a \in \mathbf{R}$
$\begin{aligned}
\therefore \quad & (1)^2-4 x y>0 \\
& 4 x y < 1
\end{aligned}$
$a x+\frac{y}{a}=1 \Rightarrow a^2 x-a+y=0$
$a \in \mathbf{R}$
$\begin{aligned}
\therefore \quad & (1)^2-4 x y>0 \\
& 4 x y < 1
\end{aligned}$
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