First slide

Equation of line in Straight lines

Question

$qx + py + (p + q - r) = 0$ is the reflection of the line $px + qy + r =0$ in the line

Moderate

A

$x - y = p + q$
B

$x - y = p - q$
C

$x + y + 1 = 0$
D

$x + y - 1 = 0$

Solution

Equation of the bisectors of the angle between the given lines are
$\frac{p x + q y + r}{\sqrt{p^{2} + q^{2}}} = \pm \frac{q x + p y + (p + q - r)}{\sqrt{p^{2} + q^{2}}}$
Taking the negative sign we get $x + y + 1 = 0$
so one is the reflection of the other line, in the line $x + y + 1 = 0$ .

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