The locus of the centre of the circle which touch the circle |z - z1| = a and |z - z2| = b externally, where z, z1, z2 are complex numbers will be

Question

The locus of the centre of the circle which touch the circle |z - z1| = a and |z - z2| = b externally, where z, z1, z2 are complex numbers will be (A) a hyperbola (B) an ellipse (C) a circle (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5e0a070e2c8f6fca67d10ac1e119d258-.png" /> |AP| = a + r |BP| = b + r Now, |AP| - |BP| = a - b ||AP|-|BP || = |a - b| Which represents a hyperbola.

Q. The locus of the centre of the circle which touch the circle $∣ z - z_{1} ∣ = a$ and $∣ z - z_{2} ∣ = b$ externally, where $z, z_{1}, z_{2}$ are complex numbers will be

a hyperbola

an ellipse

a circle

None of these

$∣ A P ∣ = a + r$
$∣ BP ∣ = b + r$
Now, $∣ A P ∣ - ∣ BP ∣ = a - b$
$∣∣ A P ∣ - ∣ BP ∣∣ = ∣ a - b ∣$
Which represents a hyperbola.

Q. The locus of the centre of the circle which touch the circle ∣z−z1​∣=a and ∣z−z2​∣=b externally, where z,z1​,z2​ are complex numbers will be