Q. If $z$ is a complex number in the Argand plane, then the equation $|z - 2|^{2} + |z + 2|^{2} = 8$ represents
A) A parabola
B) An ellipse
C) A hyperbola
D) A circle
Explanation
(d)
Given, $|x + iy - 2| + |x + iy + 2| = 8$
$\Rightarrow \ \ \ \ (x - 2)^{2} + y^{2} + (x + 2)^{2} + y^{2} = 8$
$\Rightarrow \ \ \ \ x^{2} - 4x + 4 + y^{2} + x^{2} + 4x + 4 + y^{2} = 8$
$\Rightarrow \ \ \ \ \ x^{2} + y^{2} = 0$
Which represents a circle whose radius is zero.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.