consider the points A=(0,1) and B=(2,0).let P be a point on the line 4x+3y+9=0.find the coordinate of P such that |PA-PB| is maximum

Hi Rahul,

You can calculate the coordinate of P by following the below approach :

let P be (h,k)

PA = root(h² + (k - 1)²)

PB = root((h - 2)²  + k²)

let S = |PA-PB| = root(h² + (k - 1)²)  -  root((h - 2)²  + k²)      ---- eqn (1)

Since P lies on given line therefore , 4h + 3k + 9 = 0

Put k from this eqn into eqn(1)

and differentiate S w.r.t to h

S will be maximum when dS/dh = 0 and d²S/dh² < 0.

Thus u will get vaule of h.

Please feel free to ask as mnay questions you have.

Puneet