Answer:
Given, PA = PB \[\Rightarrow \] \[\sqrt{{{(x-5)}^{2}}+{{(y-1)}^{2}}}=\sqrt{{{(x+1)}^{2}}+{{(y-5)}^{2}}}\] Squaring both sides \[{{(x-5)}^{2}}+{{(y-1)}^{2}}={{(x+1)}^{2}}+{{(y-5)}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+25-10x+{{y}^{2}}+1-2y={{x}^{2}}+1+2x+{{y}^{2}}+25-10y\] \[\Rightarrow \] \[-10x-2y=2x-10y\] \[\Rightarrow \] \[-10x-2x=-10y+2y\] \[\Rightarrow \] \[12x=8y\] \[\Rightarrow \] \[3x=2y\] Hence Proved.
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