ApplicationHardQuestion 230021
Question
If z = x + iy satisfies |z + 1| = 2|z − 1|, then the locus is:
- AA circleCorrect
- BA line
- CAn ellipse
- DA parabola
Correct answer
A circle
Explanation
|z+1|² = 4|z−1|². (x+1)² + y² = 4[(x−1)² + y²]. x² + 2x + 1 + y² = 4x² − 8x + 4 + 4y². 3x² + 3y² − 10x + 3 = 0 → x² + y² − (10/3)x + 1 = 0. This is a circle (coefficient of x² = coefficient of y²).