Question:
The locus of the mid-point of a chord of the circle $x^2 + y^2 = 4$ which subtends a right angle at the origin is:
The locus of the mid-point of a chord of the circle $x^2 + y^2 = 4$ which subtends a right angle at the origin is:
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Understanding the perpendicularity condition simplifies locus problems.
Updated On: Mar 26, 2025
- $x + y = 2$
- $x^2 + y^2 = 1$
- $x^2 + y^2 = 2$
- $x + y = 1$
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The Correct Option is C
Solution and Explanation
Let the mid-point of the chord be $(h,k)$. The perpendicular from the origin to the chord satisfies:
\[
OC = \sqrt{h^2 + k^2},
\]
Using trigonometry and given conditions, we derive:
\[
h^2 + k^2 = 2
\]
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