The locus of a point z in the Argand plane th | vedclass

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(D) Let $F_1$ be the point $(1, -1)$ and $F_2$ be the point $(2, 1)$.The given equation is $|z - F_1| - |z - F_2| = 3$,which represents the difference

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none of the above

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(D) Let $F_1$ be the point $(1, -1)$ and $F_2$ be the point $(2, 1)$.The given equation is $|z - F_1| - |z - F_2| = 3$,which represents the difference of distances from two fixed points.The distance between the foci $F_1$ and $F_2$ is $d = |F_1F_2| = \sqrt{(2 - 1)^2 + (1 - (-1))^2} = \sqrt{1^2 + 2^2} = \sqrt{5}$.For a hyperbola defined by $|PF_1 - PF_2| = 2a$,the condition $2a Here,$2a = 3$ and $d = \sqrt{5} \approx 2.236$.Since $3 > \sqrt{5}$,the condition $2a Therefore,no such point $z$ exists in the Argand plane that satisfies the given equation.

The locus of a point $z$ in the Argand plane that moves satisfying the equation $|z - (1 - i)| - |z - (2 + i)| = 3$ is:

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