First slide

Equation of line in Straight lines

Question

Reflection of the line $x + y + 1 = 0$ in the line $l x + m y + n = 0$ is

Moderate

A

$(x + y + 1) (l + m) - 2 (l^{2} + m^{2}) (l x + m y + n) = 0$
B

$(x + y + 1) (l^{2} + m^{2}) - 2 (l + m) (l x + m y + n) = 0$
C

$(l + m + 1) (x + y) - 2 (l x + m y) (l^{2} + m^{2}) = 0$
D

none of these

Solution

Required line is
$(x + y + 1) + λ (l x + m y + n) = 0$ such that $l x + m y + n = 0$
is equally inclined to $x + y + 1 = 0$ and this line.

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