question_answer

The locus of the moving point P, such that 2PA = 3PB where A is (0, 0) and B is \[\left( 4,-\,3 \right),\] is

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)  \[5{{x}^{2}}+5{{y}^{2}}-72x+54y+225=0\]

E)  None of these