If $| z - 4 i | - | z + 4 i | = 2$ then the locus of $z$ is

Circle

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Pair of lines

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Ellipse

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Hyperbola

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Solution

The correct option is D Hyperbola
$| z - 4 i | - | z + 4 i | = 2$
Clearly $| 4 i - (- 4 i) | = | 8 i | = 8 \neq 2$
Hence given expression represents a Hyperbola.
Note: The equation $| z - z_{1} | - | z - z_{2} | = k$
represents a Hyperbola if $| z_{1} - z_{2} | \neq k$

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Similar questions

| z - 4 i | + | z + 4 i | = 10

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| z + 4 i | + | z - 4 i | = 10

(\frac{z + 2}{z - 4 i}) = \frac{π}{2}

z_{1} = 3 + 4 i

z_{2} = - 3 - 4 i

| z - z_{1} | + | z - z_{2} | = 10

z ¯ ¯ ¯ z + (3 - 4 i) z + (3 + 4 i) ¯ ¯ ¯ z = 0

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