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Options

A. `x^(2)+(y-3)^(2)=0`
B. `x^(2)+4x+(y+3)^(2)=0`
C. `x^(2)+8x+(y-3)^(2)=16`
D. `(x+4)^(2)+(y-3)^(2)=16`

Answer

D

Explanation

Let the coordinates of P be (h, k) . Then, B is the mid-point of AP. So, the coordinates of B are `(h)/(k), (k+3)/(2))`.

Since B lies on the circle `x^(2)+4x+(y-3)^(2)=0`
`:. (h^(2))/(4)+4((h)/(2))+((k+3)/(2)-3)^(2)=0 rArr h^(2) + 8h + (k-3)^(2)=0`
Hence, the locus of P (h, k) is ` x^(2)+8x+(y-3)^(2)=0`.