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Consider a family of lines (4a+3)x-(a+1)...

Consider a family of lines `(4a+3)x-(a+1)y-(2a+1)=0` where `a in R` a member of this family with positive gradient making an angle of 45 with the line `3x-4y=2`, is

A

`7x-y-5=0`

B

`4x-3y+2=0`

C

`x+7y=15`

D

`5x-3y-4=0`

Text Solution

Verified by Experts

The correct Answer is:
A
`tan(45^(@))=|((4a+3)/(a+1)-(3)/(4))/(1+(12a+9)/(4a+4))|=((16a+12-3a-3)/(16a+13))`
`(13a+9)/(16a+13)=1`
`13a+9=16a+13` or `29a=-12`
`3a=-4impliesa=(-4)/(3)" "a=(-12)/(29)`
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