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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) |
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