You visited us 1 times! Enjoying our articles? Unlock Full Access!

Finding Roots of Quadratic

The locus of ...

Question

The locus of the centre of a circle which touches the circles $| z - z_{1} | = a a n d | z - z_{2} | = b$ externally is

an ellipse

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a hyperbola

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

circle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
a hyperbola

$| z - z_{1} | = a + r, | z - z_{2} | = b + r | z - z_{1} | - | z - z_{2} | = a - b$

Locus is a hyperbola with foci at $Z_{1} & Z_{2}$

Suggest Corrections

Similar questions

| z - z_{1} | = a a n d | z - z_{2} | = b

z, z_{1}, a n d z_{2}

| z - z_{1} | = a

| z - z_{2} | = b

z, z_{1}, z_{2}

| z - z_{1} | - | z - z_{2} | < | z_{2} - z_{1} |

\Rightarrow z

| z - z_{1} | = a

| z - z_{2} | = b

z_{1}, z_{2}, ϵ C)

| z - z_{1} | = a a n d | z - z_{2} | = b

z, z_{1}, a n d z_{2}

x^{2} + y^{2} = a^{2}

x^{2} + y^{2} = 4 a x

Join BYJU'S Learning Program