A variable line `L = 0` is drawn through `O(0, 0)` to meet the lines `L_1 : x + 2y - 3 = 0 and L_2 : x + 2y + 4 = 0` at points `M and N` respectively. A point `P` is taken on `L = 0` such that `1/(OP^2) = 1/(OM^2)+1/(ON^2),` then locus of point `P` is

A variable line L=0 is drawn through O(0,0) to meet the lines L:x+2y-3=0 and L:x+2y+4=0 at points M and N respectively.A point P is taken on L=0 such that (1)/((OP)^(2))=(1)/((OM)^(2))+(1)/((ON)^(2)). Locus of P is

A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y = 5 and L2: 2x + 3y = 10 at point P and Q, respectively. A point R is taken on L such that 2OP.OQ = OR.OP + OR.OQ. Locus of R is

A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. A point P IS taken on L such that 2//OP=1//OA+1//OB . Then the locus of P is

A variable line L si drawn through O(0,0) to meet lines L_1 and L_2 " given by " y-x-10=0 and y-x-20=0 at point A and B, respectively. Locus of P, if OP^2=OAxxOB , is

A variable line L is drawn through O (0,0) to meet the lines L 1 ​ :y−x−10=0 and L 2 ​ :y−x−20=0 at the points A and B respectively. A point P is taken on L such that OP 2 ​ = OA 1 ​ + OB 1 ​ and P,A,B lies on same side of origin O. The locus of P is

A variable line L is drawn through O (0,0) to meet the lines L 1 ​ :y−x−10=0 and L 2 ​ :y−x−20=0 at the points A and B respectively. A point P is taken on L such that OP 2 ​ = OA 1 ​ + OB 1 ​ and P,A,B lies on same side of origin O. The locus of P is

A variable line L is drawn through O(0,0) to meet the line L_(1) " and " L_(2) given by y-x-10 =0 and y-x-20=0 at Points A and B, respectively. Locus of P, if OP^(2) = OA xx OB , is

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: