First slide

Equation of line in Straight lines

Question

The diagonals of the parallelogram whose sides are lx + my + n = 0, lx + my + n′ = 0, mx + ly + n = 0, mx + ly + n′ = 0 include an angle

Moderate

A

$\frac{π}{3}$
B

$\frac{π}{2}$
C

$\tan^{- 1} (\frac{l^{2} - m^{2}}{l^{2} + m^{2}})$
D

$\tan^{- 1} (\frac{2 l m}{l^{2} + m^{2}})$

Solution

Since the distance between the parallel lines lx + my + n = 0 and lx + my + n′ = 0 is same as the distance between the parallel lines mx + ly + n = 0 and mx + ly + n′ = 0. Therefore, the parallelogram is a rhombus. Since the diagonals of a rhombus are at right angles, therefore the required angle is $\frac{π}{2}$ .

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