The locus of the point representing the complex number $z$ for which $|z+3|^2-|z-3|^2=15$ is

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Aicharya · Accepted Answer

Let the comlex number, $z=x+i y$ Now, $|z+3|^2-|z-3|^2=15$ $\begin{aligned} & 	herefore \quad|x+i y+3|^2-|x+i y-3|^2=15 \ & (x+3)^2+y^2-(x-3)^2-y^2=15 \ & x^2+6 x+9-x^2+6 x-9=15 \ & 12 x=15 \Rightarrow 4 x=5 \end{aligned}$ $	herefore$ It represents a straight line.

The locus of the point representing the complex number $z$ for which $|z+3|^2-|z-3|^2=15$ is

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