The points represents the complex numbers $z$, for which $|z - a|^{2} + |z + a|^{2} = b^{2}$ lie on

Question

Dr. Abubacker · Accepted Answer

(b)
Given, $\left| (x - a) + iy \right|^{2} + \left| (x + a) + iy \right|^{2} = b^{2}$
(where $z = x + iy$)
$\Rightarrow \ \ \ \ \ (x - a)^{2} + y^{2} + (x + a)^{2} + y^{2} = b^{2}$
$\Rightarrow \ \ \ \ \ \ \ \ \ x^{2} + y^{2} = \frac{b^{2} - 2a^{2}}{2}$
Hence, it represents a equation of circle

Q. The points represents the complex numbers $z$, for which $|z - a|^{2} + |z + a|^{2} = b^{2}$ lie on

Explanation

Reviewed by Dr. Abubacker

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