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 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 is (3) if (1)/((OP)^(2))=(1)/((OA)^(2))+(1)/((OB)^(2)) then locus of point P is:

A straight line through the point A(1,1) meets the parallel lines 4x+2y=9&2x+y+6=0 at points P and Q respectively.Then the point A divides the segment PQ in the ratio:

A line is a drawn from P(4,3) to meet the lines L_1 and l_2 given by 3x+4y+5=0 and 3x+4y+15=0 at points A and B respectively. From A , a line perpendicular to L is drawn meeting the line L_2 at A_1 Similarly, from point B_1 Thus a parallelogram AA_1 B B_1 is formed. Then the equation of L so that the area of the parallelogram AA_1 B B_1 is the least is (a) x-7y+17=0 (b) 7x+y+31=0 (c) x-7y-17=0 (d) x+7y-31=0

If the line y=mx meets the lines x+2y-1=0 and 2x-y+3=0 at the same point, then m is equal to

Consider the lines give by L_1: x+3y -5=0, L_2:3x - ky-1=0, L_3: 5x +2y -12=0