Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The equation of the locus of the middle point of a chord of the circle x 2 + y 2 = 2(x + y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is-
Text Solution
Verified by ExpertsThe correct answer is:
A
Solving y = mx and x 2 + y 2 – 2x – 2y = 0, we get
x 2 + m 2 x 2 – 2x – 2mx = 0
⇒ x = 0, 
Similarly, solving y = –mx and the equation of the circle, we get
x = 0, 
∴ A = 
and B = 
Let the middle point of AB be ( α , β ). Then
α = 
and
β = 
∴ α = 
, β = 
. Eliminating m from these,
α + β = 2.
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