if the circles cut orthogonally then

(distance between centres)^2 = (radius1)^2 + (radius2)^2  ------------------1  (from pythagoras theorem see figure)

now let the centre be (m,n)

therefore from 1

m^2 + n^2 = k^2 + (p - m)^2 + (q - n)^2

therefore 2pm + 2qn -(k^2 + p^2 + q^2) = 0

hence locus is 2px + 2 qy - ( p² + q² + k²) = 0 = a)