Question

In a complex plane the points A and B are at z₁ = 5 – 2i and z₂ = 1 + i. If P(z) moves such that |z – z₁| = 2|z – z₂|, then the maximum area of ΔPAB is
1. \(\frac{1}{3}\)
2. \(\frac{{25}}{3}\)
3. \(\frac{{50}}{3}\)
4. 50

Answer 1

Correct Answer - Option 2 : \(\frac{{25}}{3}\)

z lies on the circle with centre \(\left( {-\frac{1}{3},\,2} \right)\) and radius = \(\frac{{10}}{3}\)

so maximum area of ΔPAB = \(\frac{1}{2}.\frac{{10}}{3}.5 = \frac{{25}}{3}\)

z₁, z₂ and centre of circle are collinear here maximum height of triangle is radius of circle.