| Locus of the points equidistant from the points \[(-\,\,1,-1)\]and (4, 2) is |
A) \[5x-3y-9=0\]
B) \[5x+3y+9=0\]
C) \[5x+3y-9=0\]
D) \[5x-3y+9=0\]
E) None of these
Correct Answer: C
Solution :
| Let \[A\,\,(-1,-1),\]\[B\,\,(4,2)\]and \[P\,\,(x,y)\] be the points such that |
| \[A{{P}^{2}}=B{{P}^{2}}\] |
| \[\therefore \] \[{{(x+1)}^{2}}+{{(y+1)}^{2}}={{(x-4)}^{2}}+{{(y-2)}^{2}}\] |
| \[({{x}^{2}}+1+2x+{{y}^{2}}+1+2y)\] |
| \[=({{x}^{2}}+16-8x+{{y}^{2}}+4-4y)\] |
| \[\Rightarrow \] \[2+2x+2y=20-8x-4y\] |
| \[\Rightarrow \]\[10x+6y-18=0\] |
| \[\Rightarrow \]\[5x+3y-9=0\] |
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