A line passing through the point of inte...

A line passing through the point of intersection of `x+y=4` and `x-y=2` makes an angle `tan^(-1)((3)/(4))` with the x-axis. It intersects the parabola `y^(2)=4(x-3)` at points `(x_(1), y_(1))` and `(x_(2), y_(2))` respectively. Then `|x_(1)-x_(2)|` is equal to ,

A

`(16)/(9)`

B

`(32)/(9)`

C

`(40)/(9)`

D

`(80)/(9)`

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