A) \[2x+y-5=0\]
B) \[2x+y+10=0\]
C) \[2x-y-10=0\]
D) \[2x-y+10=0\]
Correct Answer: A
Solution :
| [a] Let \[A\,(-1,\,\,2)\] and \[B\,(3,\,\,4)\] and \[p\,(x-y)\]be such that |
| \[P{{A}^{2}}=P{{B}^{2}}\] |
| \[\Rightarrow \] \[{{(x+1)}^{2}}+{{(y-2)}^{2}}={{(x-3)}^{2}}+{{(y-4)}^{2}}\] |
| \[\Rightarrow \]\[{{x}^{2}}+1+2x+{{y}^{2}}+4-4y={{x}^{2}}+9-6x\] |
| \[+\,{{y}^{2}}+16-8y\] |
| \[\Rightarrow \] \[2x+5-4y=-\,6x-8y+25\] |
| \[\Rightarrow \] \[8x+4y-20=0\] |
| \[\Rightarrow \] \[2x+y-5=0\] |
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