A) \[(1,0)\]
B) \[(-2,0)\]
C) \[(3,0)\]
D) \[(4,0)\]
Correct Answer: C
Solution :
| [c] Let required point be \[P(x,0)\] |
| Also. let \[A\equiv (-3,4)\]and \[B\equiv (7,6)\] |
| \[\therefore \,\,\,\,\,\,\,\,AP=BP\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,A{{P}^{2}}=B{{P}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,{{(x+3)}^{2}}+{{(0-4)}^{2}}={{(x-7)}^{2}}+{{(0-6)}^{2}}\] |
| (By distance formula) |
| \[\Rightarrow \,\,\,\,\,\,{{x}^{2}}+9+6x+16={{x}^{2}}+49-14x+36\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,20x=60\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=3\] |
| \[\therefore \]Point \[P(3,0).\] |
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