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 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 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 drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that (OP)^(2) = OA . OB,

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 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:

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:

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