Let z ∈ C , the set of complex numbers. Then the equation, 2 z + 3 i - z - i = 0 represents:

Let z∈C, the set of complex numbers. Then the equation, 2z+3i-z-i=0 represents:
  1. A circle with radius 83
  2. An ellipse with length of minor axis 169
  3. An ellipse with length of major axis 163
  4. A circle with diameter 103

Solution

Let z=x+iy so that

2x+iy+3=x+iy-1

⇒2x2+y+32 = x2+y-12

⇒4x2+4y+32=x2+y-12

⇒3x2+3y2+26y+35=0

⇒x2+y2+263y+353=0

⇒r= 0+1699-353

⇒r=649=83

Asked in: JEE Main 2017 (08 Apr Online)

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