Locus of the points which are at equal distance from `3x + 4y-11 = 0` and `12x + 5y + 2= 0` and which is near the origin is:

Options

A. `21x - 77y +153 = 0`
B. `99x +77y - 133 = 0`
C. `7x - 11y = 19`
D. None of these

Answer

B

Explanation

Points which at equal distance from `3x +4y -11 = 0` and `12x +5y +2 = 0` lie on the angle bisector of the lines. Now given two lines are on opposite sides with respect to origin. Since required line is near to the origin, we have to find the bisector of the angle containing the origin, which is
`(2x+4y -11)/(5) =- ((12x +5y+2)/(13))` or `99x +77y - 133 =0`