﻿ The locus of the centre of a circle which touches the circles |z – z1| =a and |z – z2| = b externally (z, z1 and z2 are complex numbers) will be : Kaysons Education

# The Locus Of The Centre Of A Circle Which Touches The Circles |z – Z1| =a And |z – Z2| = B Externally (z, Z1 and Z2 are Complex Numbers) Will Be

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## Question

### Solution

Correct option is

None of These

Let A (z1), B(z2) be the centres of given circles and p be the centre of the variable circle which touches given circles externally , then

|AP| = a + r and |BP| = b + r, where are is the radius of the variable circle. On subtraction, we get |AP| – |BP| = a – b

(i)    right bisector of [AB] if a = b.

(ii)   a hyperbola if |a – b| < | AB | = |z2 – z1|

(iii)  an empty set if |a – b| > |AB| = |z2 – z1|

(iv)  Set of all points on line AB except those which lie between  and B if |a – b| = |AB| ≠ 0.

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