| If the point \[(x,y)\]is equidistant from par\[(7,1)\]and \[(3,5),\]find \[(x-y).\] |
A) 2
B) 4
C) 6
D) 8
E) None of these
Correct Answer: A
Solution :
| Let p \[(x,y)\]be equidistant from point A (7, 1) and B (3, 5). |
| \[AP=BP\]So, \[A{{P}^{2}}=B{{P}^{2}}\] |
| \[\therefore \]\[{{(x-7)}^{2}}+{{(y-1)}^{2}}={{(x-3)}^{2}}+{{(y-5)}^{2}}\] |
| \[\Rightarrow \]\[{{x}^{2}}-14x+49+{{y}^{2}}-2y+1={{x}^{2}}-6x\] \[+\,\,9+{{y}^{2}}-10y+25\] |
| \[\Rightarrow \] \[(x-y)=2\] |
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