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If the lines y = 3x + 1 and 2y = x + 3 a...

If the lines `y = 3x + 1` and `2y = x + 3` are equally inclined to the line `y=mx +4 , (1/2 < m < 3)` then find the values `m`

A

`(1+3sqrt(2))/(7)`

B

`(1-3sqrt(2))/(7)`

C

`(1+-3sqrt(2))/(7)`

D

`(1+-5sqrt(2))/(7)`

Text Solution

Verified by Experts

The correct Answer is:
D
`m_(1) = 3, m_(2)= (1)/(2)`, and `m_(3) = m`
Let the angle between first and third line is `theta_(1)` and between second and third is `theta_(2)`. Then
`tan theta_(1) =(3-m)/(1+3m)` and `tan theta_(2) = (m-(1)/(2))/(1+(m)/(2))`
But `theta_(1)= theta_(2) rArr (3-m)/(1+3m) = (m-(1)/(2))/(1+(m)/(2))`
`rArr 7m^(2) - 2m - 7 = 0 rArr m = (1+-5sqrt(2))/(7)`.
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