Let z = x + iy where x, y are real variables and If |2z – 1| = |z
| Let z = x + iy where x, y are real variables and If |2z – 1| = |z – 2| then the point z describes:
If |2z – 1| = |z – 2| then the point z describes:
A. A circle
B. An ellipse
C. A hyperbola
D. A parabola
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
|2z – 1| = |z – 2|
|2(x + iy) – 1| = |x + iy – 2|
|(2x – 1) + 2yi| = |(x – 2) + iy|
Squaring both sides
4
It is the equation of the circle.
The point z describes a circle.
