A) \[(2,0)\]
B) \[(0,2)\]
C) \[(3,0)\]
D) \[(2,2)\]
Correct Answer: A
Solution :
| [a] Let required point be \[P(x,0)\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,AP=BP\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,A{{P}^{2}}=B{{P}^{2}}\] |
| \[\Rightarrow \,\,{{(x+1)}^{2}}+{{(0-0)}^{2}}={{(x-5)}^{2}}+{{(0-0)}^{2}}\] |
| \[\Rightarrow \,\,{{x}^{2}}+1+2x+0={{x}^{2}}+25-10x+0\] |
| \[\Rightarrow \,\,\,\,12x=24\] |
| \[\Rightarrow \,\,\,\,x=2\] |
| \[\therefore \,\,\,\,\,P\equiv (2,0)\] |
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