If the coordinates of two points `A` and `B` are (3, 4) and `(5,-2)` , respectively, find the coordinates of any point `P` if `P A=P Bdot` Area of ` P A B` is 10 sq. units.

Explanation

Let the coordinates of point P be `(x,y)`
Given that `PA=PB`
or ` PA^2=PB^2`
`rArr(x-3)^2+(y-4)^2=(x-5)^2+(y+2)^2`
`rArrx-3y-1=0`
`rArr(1)/(2)||{:(x,,y,,),(3,,4,,),(5,,-2,,),(x,,y,,):}||=10`
`rArr6x+2y-26=+-20`
`rArr3x+y-23=0" "(2)`
or `3x+y-3=0" " (3)`
Solving (1) and (2), we get `x=7,y=2`
Solving (1) and (3), we get `x=1,y=0`.
Thus, the coordinates of P can be `(7,2) or (1,0)` .