Question

The intercepts on the straight line $y=mx$ by the line $y=2$ and $y=6$ is less than 5 , then $m$ belongs to

• A. $]-\frac{4}{3},\frac{4}{3}[$
• B. $]\frac{4}{3},\frac{3}{8}[$
• C. $]-\infty ,-\frac{4}{3}[\cup ]\frac{4}{3},\infty [$
• D. $]\frac{4}{3},\infty [$

Answer 1

Answer: (C)

Given lines are $y=mx,y=2$ 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]
$\Rightarrow {\left(\frac{2}{m}-\frac{6}{m}\right)}^2+(4{)}^2<25$
$\Rightarrow {\left(\frac{2}{m}-\frac{6}{m}\right)}^2<9$
$\Rightarrow -3<\frac{2}{m}-\frac{6}{m}<3$
$\Rightarrow -\frac{4}{3}>m>\frac{4}{3}$
$\therefore m\in ]-\infty ,-\frac{4}{3}[\cup ]\frac{4}{3},\infty [$