First slide

Equation of line in Straight lines

Question

If two lines $4 x + 3 y + 5 = 0$ and $l x + m y + 4 = 0$ are the angular bisectors of two lines then the relation between $l, m$ is

Moderate

A

$4 l - 3 m = 0$
B

$3 l - 4 m = 0$
C

$2 l - 3 m = 0$
D

$l - m = 0$

Solution

$The angle between angular bisectors of any two intersecting lines is 90^{\circ}$
$If two lines a_{1} x + b_{1} y + c_{1} = 0 and a_{2} x + b_{2} y + c_{2} = 0 are perpendicular then a_{1} a_{2} - b_{1} b_{2} = 0$
$Here 4 x + 3 y + 5 = 0 and b x + m y + 4 = 0 are perpendicular.$
$Therefore, 4 l - 3 m = 0$

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