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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CENGAGE-COORDINATE SYSTEM-Multiple Correct Answers Type
