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Q.
The intercepts on the straight line $y=m x$ by the line $y=2$ and $y=6$ is less than 5 , then $m$ belongs to
ManipalManipal 2016
Solution:
Given lines are $y=m x, y=2$ and $y=6$.
Here, coordinates of points $A$ and $B$ are $\left(\frac{2}{m}, 2\right),\left(\frac{6}{m}, 6\right)$, respectively.
$\therefore AB =\sqrt{\left(\frac{2}{m}-\frac{6}{m}\right)^{2}+(2-6)^{2}}<5$ [given]
$\Rightarrow\left(\frac{2}{m}-\frac{6}{m}\right)^{2}+(4)^{2}<25$
$\Rightarrow\left(\frac{2}{m}-\frac{6}{m}\right)^{2}<9$
$\Rightarrow-3<\frac{2}{m}-\frac{6}{m}<3$
$\Rightarrow-\frac{4}{3}>m>\frac{4}{3}$
$\therefore m \in]-\infty,-\frac{4}{3}[\cup] \frac{4}{3}, \infty[$
