# Toronto Math Forum

## MAT334--2020F => MAT334--Lectures & Home Assignments => Chapter 1 => Topic started by: Maria-Clara Eberlein on September 23, 2020, 07:27:50 PM

Title: 1.2 circles
Post by: Maria-Clara Eberlein on September 23, 2020, 07:27:50 PM
When we have are asked to find the locus of |z-p|=|z-q|, can we immediately say the perpendicular bisector of the line segment joining p and q, or must we plug in z=x+iy and solve to get x=0?
Title: Re: 1.2 circles
Post by: shiyuancao on September 24, 2020, 04:52:59 PM
I think this depends on how you want to represent your solution. Both of them seems rational to me.
But $x$ does not necessarily to be $0$ since $p$ and $q$ are some arbitrary complex numbers.
Title: Re: 1.2 circles
Post by: Lubna Burki on September 24, 2020, 07:34:11 PM
I think it's enough to say that this looks like one of the Apollonius circles in which is row is 1 then a line is given (specifically the perpendicular bisector of the two foci).