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Question

Let Z1, Z2, Z3 be three points A, B and P respectively in the argand plane. Let P moves in the plane such that |ZZ1|+|ZZ2|=K. Let Z1=Z2=i Maximum area of the triangle ABP is (if K = 4)


  1. 2 sq. units

  2. 23 sq. units

  3. 3 sq. units

  4. 4 sq. units


Solution

The correct option is C

3 sq. units


|ZZ1|+|ZZ2|=K is the condition of an ellipse.

It is a standing ellipse with foci (0, 1) and (0, 1)

be=1  [Comparing it with standard equation of ellipse : x2a2+y2b2=1 with eccentricity, e]

b×1a2b2=1

b2a2=1

b2a2=1

Now, b=2K=4

a=3

AB=2

 Area of the triangle ABP is maximum when P is at (3, 0) or (3, 0)

So, area of the triangle ABP=12×AB×3=3 sq. units

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