Let P be a variable point on the parabol...

Let P be a variable point on the parabola `y = 4x ^(2) +1.` Then, the locus of the mid- point of the point P and the foot of the perpendicular drawn from the point P to the line y =x is:

A

`(3x- y)^(2) + (x-3y) + 2= 0`

B

`2(3x- y)^(2) + (x-3y) + 2= 0`

C

`2(x- 3y)^(2) + (3x- y)+2= 0`

D

`(3x- y)^(2) + 2(x-3y) + 2= 0`

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The correct Answer is:

B

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