If the intercepts made by the line `y=mx` by lines `x=2` and `x=5` is less than 5, then the range of values of m is a. `(-oo,-4/3)uu(4/3,oo)` b. `(-4/3,4/3)` c. `(-3/4,4/3)` d. none of these

Options

A. `(-oo, -4//3) uu (4//3, +oo)`
B. (-4/3, 4/3)
C. (-3/4,4/3)
D. none of these

Answer

A

Explanation

The distance between (2/m, 2) and (6/m, 6) is less than 5 Hence,
`((2)/(m) - (6)/(m))^(2) + (2-6)^(2) lt 25`
`"or " (16)/(m^(2)) lt 9`
`"or " m^(2) gt (16)/(9)`
`i.e., m gt (4)/(3) "or " m lt (-4)/(3)`