First slide

Equation of line in Straight lines

Question

The bisector of the acute angle formed between the lines $4 x - 3 y + 7 = 0$ and $3 x - 4 y + 14 = 0$ has the equation

Moderate

A

$x + y + 3 = 0$
B

$x - y - 3 = 0$
C

$X - y + 3 = 0$
D

$3 x + y - 7 = 0$

Solution

The equations of given straight lines, by making constant terms positive, are
$4 x - 3 y + 7 = 0 and 3 x - 4 y + 14 = 0$
$∵ 4 \times 3 + (- 3) (- 4) = 24 > 0 i.e. a_{1} a_{2} + b_{1} b_{2} > 0$
So, the bisector of the acute angle is given by
$\frac{4 x - 3 y + 7}{\sqrt{4^{2} + (- 3)^{2}}} = - \frac{3 x - 4 y + 14}{\sqrt{3^{2} (- 4)^{2}}} \Rightarrow x - y + 3 = 0$

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