From the point A(0, 3) on the circle x² + 4x + (y – 3)² = 0 a chord AB is drawn and extended to a point P such that 

AP = 2AB then the locus of P is

P = midpoint AB $=\left(\frac{\mathrm{x}}{2},\frac{\mathrm{y}+3}{2}\right)$
Put P lies on x² + 4x + (y – 3)² = 0                                    

$$\begin{gathered} \frac{x^2}{4}+2x+{\left(\frac{y+3}{2}-3\right)}^2=0 \\ \frac{x^2}{4}+2x+\frac{{{\displaystyle y}}^2-6y+9}{4}=0 \\ {x}^2+y^2+8x-6y+9=0 \end{gathered}$$