If z - x - iy- then the equation - 2 z - i-z - 1 - - k will be a straight line- where

The correct option is D k = 2 | 2 z i/z + 1 | = k ⇒ (2x)^2+(2y 1)^2=k^2((x+1)^2+y^2) above equation represents a straight line if k^2=4 ∴ ...

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Byju's Answer

Standard XII

Mathematics

Variable Separable Method

If z = x + ...

Question

If $z = x + i y$ , then the equation $∣ ∣ ∣ \frac{2 z - i}{z + 1} ∣ ∣ ∣ = k$ will be a straight line, where

k = 1

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k = 1/2

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k = 2

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k = 3

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Solution

The correct option is D k = 2
$∣ ∣ ∣ \frac{2 z - i}{z + 1} ∣ ∣ ∣ = k$
$\Rightarrow (2 x)^{2} + (2 y - 1)^{2} = k^{2} ((x + 1)^{2} + y^{2})$
above equation represents a straight line if $k^{2} = 4$
$∴ k = \pm 2$
Hence, option C.

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