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A line L is a drawn from P(4,3) to meet ...

A line `L` is a drawn from `P(4,3)` to meet the lines `L-1a n dL_2` given by `3x+4y+5=0` and `3x+4y+15=0` at points `Aa n dB` , respectively. From `A` , a line perpendicular to `L` is drawn meeting the line `L_2` at `A_1dot` Similarly, from point `B_1dot` Thus, a parallelogram `AA_1B B_1` is formed. Then the equation of `L` so that the area of the parallelogram `AA_1B 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`

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A line L is a drawn from P(4,3) to meet the lines L-1a n dL_2 given by 3x+4y+5=0 and 3x+4y+15=0 at points Aa n dB , respectively. From A , a line perpendicular to L is drawn meeting the line L_2 at A_1dot Similarly, from point B_1dot Thus, a parallelogram AA_1B B_1 is formed. Then the equation of L so that the area of the parallelogram AA_1B B_1 is the least is x-7y+17=0 7x+y+31=0 x-7y-17=0 x+7y-31=0

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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

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