z=x+i y and the point P represents z in the Argand plane. If the amplitude of (\frac{2 z-i}{z+2 i}) is \frac{\pi}{4}, then the equation of the locus of P is [TG EAPCET 11 May 2024 Shift 1]

Correct Answer is : 2x2+2y2+5x+3y−2=0,(x,y)≠(0,−2)

2 x^2+2 y^2-3 x+3 y-2=0,(x, y) \neq(0,-2)

2 x^2+2 y^2+5 x+3 y-2=0,(x, y) \neq(0,-2)

2 x^2+2 y^2+3 x+3 y-2=0,(x, y) \neq(0,2)

2 x^2+2 y^2-5 x+3 y-2=0,(x, y) \neq(0,2)

Correct Answer is : 2x2+2y2+5x+3y−2=0,(x,y)≠(0,−2)

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