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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)`

Text Solution

Verified by Experts

The correct Answer is:
B
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