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Question -

Show that the diagonals of the parallelogram whose sides are lx + my + n= 0, lx + my + n’ = 0, mx + ly + n = 0 and mx + ly + n’ = 0 include an angleπ/2.



Answer -

Given:

The given lines are

lx + my + n = 0 … (1)

mx + ly + n’ = 0 … (2)

lx + my + n’ = 0 … (3)

mx + ly + n = 0 … (4)

Let us prove, the diagonalsof the parallelogram whose sides are lx + my + n = 0, lx + my + n’ = 0, mx + ly+ n = 0 and mx + ly + n’ = 0 include an angle π/2.

By solving (1) and(2), we get

m1m2 =-1

Hence proved.

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