A) (0, 0)
B) \[\left( \frac{5}{4},0 \right)\]
C) \[\left( \frac{5}{2},0 \right)\]
D) \[\left( \frac{5}{3},0 \right)\]
Correct Answer: B
Solution :
Let the point A is (h, k) \[\frac{AP}{AQ}=\frac{1}{3}\] \[3AP=AQ\] \[\Rightarrow \]\[9A{{P}^{2}}=A{{Q}^{2}}\] \[\Rightarrow \]\[9[{{(h1)}^{2}}+{{k}^{2}}]={{(h1)}^{2}}+{{k}^{2}}\] \[\Rightarrow \]\[{{h}^{2}}+{{k}^{2}}-\frac{5}{2}h-1=0\] Locus of\[A(h,\text{ }k)\]is \[{{x}^{2}}+{{y}^{2}}-\frac{5}{2}x-1=0\] \[\therefore \] Circumcentre of\[\Delta ABC\]is \[\left( \frac{5}{4},0 \right)\]You need to login to perform this action.
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