The coordinates of two points A and Bare ( 3, 4) and (5, - 2) respectively. If P is a point not lying on any of the coordinate axes such that PA = PB and Area of of ∆PAB = 10, then the coordinates of P, are

Let the coordinates of P be (x, y). Then,PA=PB⇒ PA2=PB2⇒ (x−3)2+(y−4)2=(x−5)2+(y+2)2x−3y−1=0                                                                   ...(i)Now, Area of △PAB=10⇒ 12xy13415−21=±10⇒ 6x+2y−26=±20Solving (i) with equations in (ii), we obtain x=7,y=2 and x=1,y=0.But, P does not lie on any of the coordinate axes. Thus, the coordinates of P are (7,2)