Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find the locus of the mid point of the chord of a circle x² + y² = 4 such that the segment intercepted by the chord on the curve x² − 2x − 2y = 0 subtends a right angle at the origin.
Text Solution
Verified by ExpertsThe correct answer is:
A
Let mid-point be (h, k) ⇒ hx + ky = h 2 + k 2
subtend right angle ⇒ x 2 – 2(x + y) 
= 0 ⇒ (h 2 + k 2 ) x 2 – 2(x + y) (hx + ky) = 0
As angle 90º , Coefficient of x 2 + Coefficient of y 2 = 0 ⇒ h 2 + k 2 – 2h – 2k = 0 ⇒
Locus x 2 + y 2 – 2x –2y = 0
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