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 `(-(24)/5,(17)/5)` (b) `(-(84)/5,(13)/5)` `((31)/7,(31)/7)` (d) `(0,0)`

Explanation

To solve the problem, we need to find the coordinates of point \( P \) on the line \( 4x + 3y + 9 = 0 \) such that the absolute difference \( |PA - PB| \) is maximized, where \( A(0, 1) \) and \( B(2, 0) \).

### Step 1: Find the equation of line \( AB \)

The coordinates of points \( A \) and \( B \) are:
- \( A(0, 1) \)
- \( B(2, 0) \)

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