A variable line L is drawn through O (0, 0) to meet the lines L1 and L2 given by y + x – 15 = 0 and y + x – 30 = 0 at the points A and B, respectively. A point P is taken on L such that \(\frac{3}{\mathrm{OP}}\) = \(\frac{1}{\mathrm{OA}}\) - \(\frac{1}{\mathrm{OB}}\). Then the locus of P is –
1
x + 2y = 45
2
2x - y = 60
3
x - y = 45
4
x + y = 90