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MHT CET20242 May 2024Evening ShiftMathematicsComplex NumberActual

If P (x, y) denotes z =x+ i y x, y R and i = -1 in Argand's plane and | z-1 z+2 i |=1 , then the locus of P is

Options

  1. Aparabola
  2. Bhyperbola
  3. Ccircle
  4. Dstraight line

Correct answer

D. straight line

Step-by-step solution

aligned & | z -1 z +2 i |=1 & | x+ i y-1 x+ i y+2 i |=1 & |x-1+ i y|=|x+(y+2) i | & (x-1)^2+y^2 = x^2+(y+2)^2 & x^2-2 x+1+y^2=x^2+y^2+4 y+4 & 2 x+4 y+3=0, which is a straight line aligned

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