A) \[5{{x}^{2}}-5{{y}^{2}}-72x+54y+225=0\]
B) \[5{{x}^{2}}-5{{y}^{2}}+72x+54y+225=0\]
C) \[5{{x}^{2}}+5{{y}^{2}}+72x+54y+225=0\]
D) \[5{{x}^{2}}+5{{y}^{2}}-72x+54y+225=0\]
Correct Answer: D
Solution :
Let \[P(h,\,\,k).\] Given \[2PA=3PB\,\,\Rightarrow \,\,4P{{A}^{2}}=9P{{B}^{2}}\] \[\Rightarrow \,\,4\,({{h}^{2}}+{{k}^{2}})=9\,[{{(h-4)}^{2}}+{{(k+3)}^{2}}]\] \[\Rightarrow \,\,5{{h}^{2}}+5{{k}^{2}}-72h+54k+225=0\] Hence the locus of point P is given by \[5{{x}^{2}}+5{{y}^{2}}-72x+54y+225=0\].
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