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Equation of circle in Complex Form

If | z - z 1|...

Question

If $| z - z_{1} | + | z + z_{2} |$ = $λ, λ \in R^{+}, z_{1}, z_{2}$ are fixed complex numbers, represents an ellipse, then:

A

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B

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C

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D

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Solution

The correct option is B

Basic concept

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Similar questions

For two complex numbers $z_{1}$ and $z_{2}$ . It is given that $∣ ∣ ∣ \frac{z_{1} {- z}_{2}}{_{1} + z_{2}} ∣ ∣ ∣ = 1$ . Prove that $i \frac{z_{1}}{z_{2}} = λ$ , where $λ$ is real. Also determine the angle between the lines drawn from origin to points $z_{1} + z_{2}$ and $z_{1} - z_{2}$ .

Q. Prove that inequality:

{| z_{1} + z_{2} |}^{2} \leq (1 + λ) {| z_{1} |}^{2} + (1 + \frac{1}{λ}) {| z_{2} |}^{2}

λ > 0

| z - z_{1} | + | z - z_{2} | = k (> | z_{1} - z_{2} |)

, then the locus of

z

z_{1}

z_{2}

are fixed complex numbers)

z

| z - z_{1} | - | z - z_{2} | = λ

$If z_{1} and z_{2}$ are two complex numbers such that $| z_{1} | = | z_{2} | and (z) + a r g (z_{2}) = π, then show that z_{1} = -_{2} .$

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Equation of circle in Complex Form

Standard XI Mathematics

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