question_answer

Consider the points \[A(0,1)\] and \[B(2,0),\] and P be a point on the line \[4x+3y+9=0.\] The coordinates of P such that \[\left| PA-PB \right|\] is maximum are

A) \[(-12/5,17/5)\]

B) \[(-84/5,13/5)\]

C) \[(-6/5,17/5)\]

D) \[(0,-3)\]

Correct Answer: B

Solution :

[b] The equation of AB is \[y-1=\frac{0-1}{2-1}x\] or \[x+2y-2=0\] \[\left| PA-PB \right|\le AB\] Thus, \[\left| PA-PB \right|\] 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 \[P(-84/5,13/5).\]