Question
If the intercept made on the line $$y=mx$$ by lines $$y=2$$ and $$y=6$$ is less than 5 then the range of values of $$m$$ is :
A.
$$\left( { - \infty ,\, - \frac{4}{3}} \right) \cup \left( {\frac{4}{3},\, + \infty } \right)$$
B.
$$\left( { - \frac{4}{3},\,\frac{4}{3}} \right)$$
C.
$$\left( { - \frac{3}{4},\,\frac{3}{4}} \right)$$
D.
none of these
Answer :
$$\left( { - \infty ,\, - \frac{4}{3}} \right) \cup \left( {\frac{4}{3},\, + \infty } \right)$$
Solution :
The distance between $$\left( {\frac{2}{m},\,2} \right)$$ and $$\left( {\frac{6}{m},\,6} \right)$$ is less than 5
$$\eqalign{
& \Rightarrow {\left( {\frac{2}{m} - \frac{6}{m}} \right)^2} + {\left( {2 - 6} \right)^2} < 25 \cr
& \Rightarrow \frac{{16}}{{{m^2}}} < 9 \cr
& \Rightarrow {m^2} > \frac{{16}}{9} \cr
& \Rightarrow m > \frac{4}{3}{\text{ or }}m < \frac{{ - 4}}{3} \cr} $$