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CGP EDU Academic Team
Published on: August 14, 2026
A line of fixed lingth2 units moves so that its ends are on the positive x-axis and that part of the line x + y = 0 which lies in the second quadrant. Then the locus of the mid-point of the line has the equation-
Text Solution
Verified by ExpertsThe correct answer is:
A
If ∠ BAO = θ then BM = 2 sin θ and
MO = BM = 2 sin θ , MA = 2 cos θ
Hence A = (2 cos θ – 2 sin θ , 0) and
B = (–2 sin θ , 2 sin θ )
Since P(x, y) is the mid point of AB,
2x = (2 cos θ ) + (–4 sin θ ) or cos θ – 2 sin θ = x
2y = (2 sin θ ) or sin θ = y
Eliminating θ , we have (x + 2y) 2 + y 2 = 1 or ,
x 2 + 5y 2 + 4xy – 1 = 0.
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