A) \[{{x}^{2}}+{{y}^{2}}-y=0\]
B) \[{{x}^{2}}+{{y}^{2}}-x=0\]
C) \[{{x}^{2}}+{{y}^{2}}-2x=0\]
D) \[{{x}^{2}}+{{y}^{2}}-x-y=0\]
E) \[{{x}^{2}}+{{y}^{2}}+y=0\]
Correct Answer: A
Solution :
Let\[(h,k)\]be the midpoint of the chord drawn through the origin. Then the equation of the chord is \[hx+ky-(y+k)={{h}^{2}}+{{k}^{2}}-2k\] This passes through (0, 0) \[\therefore \] \[-k={{h}^{2}}+{{k}^{2}}-2k\] \[\Rightarrow \] \[{{h}^{2}}+{{k}^{2}}-k=0\] \[\therefore \]Locus of\[(h,k)\]is\[{{x}^{2}}+{{y}^{2}}-y=0\].
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