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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

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a hyperbola

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circle

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none

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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

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