The locus of the points represented by |z+3|- | vedclass

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(D) Given the equation $|z+3|-|z-3|=6$. Let $z = x + iy$. The points $z_1 = -3$ and $z_2 = 3$ are the foci of the hyperbola. The distance between the

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$A$ ray on the $x$-axis

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(D) Given the equation $|z+3|-|z-3|=6$. Let $z = x + iy$. The points $z_1 = -3$ and $z_2 = 3$ are the foci of the hyperbola. The distance between the foci is $2c = |3 - (-3)| = 6$. The definition of a hyperbola is $| |z - z_1| - |z - z_2| | = 2a$. Here,$2a = 6$,so $a = 3$. Since $2a = 2c$,the hyperbola degenerates into the line segment connecting the foci. Specifically,for $|z+3|-|z-3|=6$,the condition $|z+3| = |z-3| + 6$ implies that $z$ must lie on the $x$-axis to the right of $3$ (i.e.,$x \ge 3$). However,looking at the options provided,the most appropriate description for the locus defined by $|z+3|-|z-3|=6$ is a ray on the $x$-axis starting from $3$ to $\infty$.

The locus of the points represented by $|z+3|-|z-3|=6$,where $z$ is a complex number,is ....

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