Question

The locus of $z$ such that $|z-a{|}^2+|z-b{|}^2=\lambda$ is?
($a$ , $b$ and $\lambda$ are real)

• A. a circle
• B. a parabola
• C. an ellipse
• D. a pair of straight lines

Answer 1

Answer: (A)

a circle

Let $z=x+iy$

$|z-a{|}^2+|z-b{|}^2=\lambda$

$\Rightarrow (x-a{)}^2+y^2+(x-b{)}^2+y^2=\lambda$

$x^2-(a+b)x+y^2=\frac{\lambda }{2}$

This is the equation of a circle.