The locus of the centre of a circle which touches the circle

• Complex Numbers
• Coordinate Geometry

The locus of the centre of a circle which touches the circle |z - z₁| = a and |z - z₂| = b externaly (z, z₁ & z₂ are complex numbers) will be

1. a hyperbola
2. an ellipse
3. a circle
4. a straight line

Answer

z₁z₃ - z₃z₂ = (a + r) – (b + r) = a - b = constant,

which represent a hyperbola. 

Since, a hyperbola is the locus of a point which moves in such a way that the difference of its distances from two fixed points (foci) is always constant.

The correct option is A.