### Author Topic: 1.2 circles  (Read 503 times)

#### Maria-Clara Eberlein

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##### 1.2 circles
« 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?
« Last Edit: September 25, 2020, 12:11:12 AM by Maria-Clara Eberlein »

#### shiyuancao

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##### Re: 1.2 circles
« Reply #1 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.

#### Lubna Burki

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##### Re: 1.2 circles
« Reply #2 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).