A) \[(2,11)\]
B) \[(11,2)\]
C) \[(11,-2)\]
D) \[(-2,11)\]
Correct Answer: B
Solution :
Let \[P(x,y)\] be the centre of the circle passing through \[A(1,2),\,B(3,-4)\] and \[C(5,-6)\] Also, we know that, \[AP=PB=PC\] Now, we have, \[A{{P}^{2}}=P{{B}^{2}}\] \[\Rightarrow \] \[{{(x-1)}^{2}}+{{(y-2)}^{2}}\] \[={{(x-3)}^{2}}+{{(y-2)}^{2}}\] \[\Rightarrow \] \[x-3y=5\] ?..(i) Also, \[A{{P}^{2}}=C{{P}^{2}}\] \[\Rightarrow \] \[{{(x-1)}^{2}}+{{(y-2)}^{2}}\] \[={{(x-5)}^{2}}+{{(y+6)}^{2}}\] \[\Rightarrow \] \[x-2y=7\] Solving (i) and (ii), we get, \[x=22,\,\,\,y=2\] \[\therefore \] The coordinates of centre \[P=(11,2)\]You need to login to perform this action.
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