Q. 65.0( 2 Votes )
Prove that 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.
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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