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Consider the points `A(0,1)a n dB(2,0),a n dP` be a point on the line `4x+3y+9=0` . The coordinates of `P` such that `|P A-P B|` is maximum are `(-(12)/5,(17)/5)` (b) `(-(84)/5,(13)/5)` `((31)/7,(31)/7)` (d) `(,0)`

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Verified by Experts

The correct Answer is:
B

The equation of AB is
`y-1 = (0-1)/(2-1)x or x+2y-2=0`
`|PA-PB| le AB`
Thus, |PA-PB| is maximum if the points A,B, and P are collinear.
Hence, solving x+2y-2=0 and 4x+3y+9=0, we get point `P-=(-24//5, 17//5).`
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