a variable line `L` is drawn trough `O(0,0)` to meet the lines `L_1:y-x-10=0` and `L_2:y-x-20=0` at point `A&B` respectively .A point `P` is taken on line `L` the `(1) ` if `2/(OP)=1/(OA)+1/(OB)` then locus of `P` is `(2)` if `(OP)^2=(OA)*(OB)` then locus of `P` is `(3)` if `1/(OP)^2=1/(OA)^2+1/(OB)^2` then locus of point `P` is:

Options

A. `3x+3y=40`
B. `3x+3y+40=0`
C. `3x-3y=40`
D. `3y-3x=40`

Answer

D