Q82 / 160 · TS EAMCET 2020 (14 Sep Shift 1) · Mathematics

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

  • A
    $x+y>4$
  • B
    $4 x y>1$
  • Correct answer
    C
    $4 x y < 1$
  • D
    $x+y=4$

Solution

Equation of line is moving such that intercept mode by it on the coordinate axis are reciprocal to each other is $a x+\frac{y}{a}=1 \Rightarrow a^2 x-a+y=0$ $a \in \mathbf{R}$ $\begin{aligned} \therefore \quad & (1)^2-4 x y>0 \\ & 4 x y < 1 \end{aligned}$

Hence, the correct answer is option: 'C'.

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