First slide

Equation of line in Straight lines

Question

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

Moderate

A

$21 x - 77 y + 153 = 0$
B

$99 x + 77 y - 133 = 0$
C

$7 x - 11 y = 19$
D

None of these

Solution

Points which at equal distance from 3x + 4y - 11 = 0 and l2x + 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
$\frac{3 x + 4 y - 11}{5} = - (\frac{12 x + 5 y + 2}{13}) or 99 x + 77 y - 133 = 0$

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