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Q.
If the intercept made on the line $y=m x$ by lines $y=2$ and $y=6$ is less than 5 , then the range of values of $m$ is
Straight Lines
Solution:
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 $m<\frac{-4}{3}$