MixedMediumQuestion 320013
Question
The locus of the midpoints of all chords of x²+y²=r² that subtend a right angle at the centre is:
- Ax²+y²=r²/2Correct
- Bx²+y²=r²
- Cx+y=r
- Dx²−y²=r²
Correct answer
x²+y²=r²/2
Explanation
If chord subtends 90° at centre (0,0) and midpoint is (h,k): OA⊥OB and OA=OB=r. The midpoint M satisfies OM=r/√2 → OM²=r²/2 → h²+k²=r²/2. Locus: x²+y²=r²/2.