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. $(-\infty ,-4/3)\cup (4/3,+\infty )$
• B. $(-4/3,4/3)$
• C. $(-3/4,4/3)$
• D. none of these

Answer 1

Answer: (A)

The distance between $(2/m,2)$ and $(6/m,6)$ is less than 5 . Hence,
${\left(\frac{2}{m}-\frac{6}{m}\right)}^2+(2-6{)}^2<25$
or $\frac{16}{m^2}<9$
or $m^2>\frac{16}{9}$
i.e., $m>\frac{4}{3}$ or $m<\frac{-4}{3}$