Question

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

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.

SIMILAR QUESTIONS

Q1
Q3
Q4

The point represented by the complex number 2 – I is rotated about origin through an angle in the clockwise direction. The complex number corresponding to new position of the point is

Q5

                                    

Q6

For all complex number z1, z2 satisfying |z1| = 12 and |z2 – 3 – 4i| = 5, the minimum value of |z1 – z2| is

Q7
Q9

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin, then n must be on then form