A) \[{{x}^{2}}+{{y}^{2}}=\frac{3}{2}\]
B) \[{{x}^{2}}+{{y}^{2}}=1\]
C) \[{{x}^{2}}+{{y}^{2}}=\frac{27}{4}\]
D) \[{{x}^{2}}+{{y}^{2}}=\frac{9}{4}\]
Correct Answer: D
Solution :
Let \[M(h,k)\] be the mid-point of chord AB where |
\[\angle ACB=\frac{2\pi }{3}\] \[\therefore \angle ACM=\frac{\pi }{3}\] |
Also \[CM=3\,\cos \frac{\pi }{3}=\frac{3}{2}\] |
\[\Rightarrow \,\sqrt{{{h}^{2}}+{{k}^{2}}}=\frac{3}{2}\Rightarrow {{h}^{2}}+{{k}^{2}}=\frac{9}{4}\] |
\[\therefore \] Locus of \[(h,k)\] is \[{{x}^{2}}+{{y}^{2}}=\frac{9}{4}\] |
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