Answer :

Given:


Lines represented by x(1 + λ) + y(2 – λ) + 5 = 0, λ being arbitrary


To prove:


The family of lines represented by x(1 + λ) + y(2 – λ) + 5 = 0, λ being arbitrary, pass through a fixed point. Also, find the fixed point.


Explanation:


The given family of lines can be written as


x + 2y + 5 + λ (x y) = 0


This line is of the form L1 + λL2 = 0, which passes through the intersection of L1 = 0 and L2 = 0.
x + 2y + 5 = 0
x y = 0


Now, solving the lines:
This is a fixed point.


Hence proved.


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