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MHT CET202521 Apr 2025Evening ShiftMathematicsComplex NumberActual

The locus of the points represented by |z+3|-|z-3|=6 , where z is a complex number, is ....

Options

  1. ACircle with radius 1 unit
  2. BStraight line with slope 1.
  3. CParabola with focus (1,0)
  4. DX-axis

Correct answer

D. X-axis

Step-by-step solution

Let z = x + iy with x, y R . The equation |z+3| - |z-3| = 6 describes a set of points where the difference of distances to F₁ = -3 and F₂ = 3 is constant. This defines a hyperbola, but with 2a = 6 and 2c = |F₁ - F₂| = 6 , a = c = 3 implies the hyperbola degenerates. The condition |z - F₁| - |z - F₂| = |F₁ - F₂| requires that z lies on the x-axis with F₂ between F₁ and z , so y=0 . Substituting z = x , the equation becomes |x+3| - |x-3| = 6 . For x 3 , |x+3| - |x-3| = (x+3) - (x-3) = 6 , which holds. For x The locus

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