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Algebra
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10 Nov 2019

A and b are two fixed points in the plane; k is a fixedrealnumber. Find the locus of points P for which
PA2 + PB2=k
What condition must k satisfy for this locus not to be anemptyset?
P(x,y)
A
(a1,a2) B
(b1,b2)
Denote p=<x,y>,A=<a1,a2>,andB=<b1,b2>
We need to show that it is indeed the equation of acircle.Certainly k cannot be arbitrary: if k<0 then the locus isemptysince in that case PA2+PB2 =k cannotpossiblybe satisfied by any point.
So PA2 + PB2 = k
(x-a1)2 +(y-a2)2+(x-b1)2+(y-b2)2=k
PA2 + PB2 =k
At this point can I get some help of what the answer tomultiplyingout the equation would be
also and explanation of what k has to be?

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Thanks. I have a lot ofpoints for this and will give it to someone that can helpme.

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