Let A 3 - i , B 2 + i be two points in the Argand plane. If the point P represents the complex number z = x…

Let A3-i,B2+i be two points in the Argand plane. If the point P represents the complex number z=x+iy, which satisfies z-3+i=z-2-i, then the locus of the point P is
  1. the circle with AB as diameter
  2. the line passing through A and B
  3. the perpendicular bisector of AB
  4. the ellipse with AB as major axis

Solution

Given,

A3-i⇒A≡3,-1

B2+i⇒B≡2,1

Now,

z-3+i=z-2-i

⇒z-3-i=z-2+i≡z-A=z-B

⇒z-3-i=z-2+i≡P-A=P-B

Therefore, we get AP=BP.

Point P is moving along the line CM such that AP=BP.

Hence, locus of the point P is the perpendicular bisector of line AB.

Asked in: AP EAMCET 2018 (25 Apr Shift 1)

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