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$\frac{| z - z_{1} |}{| z - z_{2} |} = k$ ,(k > 1) represents

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a circle for which $z_{1}$ lies outside $z_{2}$ lies inside the circle

a circle for which $z_{1}$ and $z_{2}$ are interior points

a circle for which $z_{1} & z_{2}$ lie outside the circle

a circle for which $z_{1}$ lies inside and $z_{2}$ lies outside the circle

answer is D.

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Detailed Solution

$L e t A = z_{1} a n d B = z_{2}$

If $\frac{P A}{P B} = k (k > 1)$ ,the circle devides AB in the ratio k : 1 .

Since PA $>$ PB $\Rightarrow$ P is close to B than A.

Hence B lies inside and A lies out side the circle

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