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Show that the locus of the centres of a circle which cuts two given circles orthogonally

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Show that the locus of the centres of a circle which cuts two given circles orthogonally is a straight line & hence deduce the locus of the centres of the circles which cut the circles x2 + y2 + 4x – 6y + 9 = 0 & x2 + y2 – 5x + 4y + 2 = 0 orthogonally. Intercept the locus.

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Let the circle orthogonal to the two circles be 

Which is the radical axis & (straight line) 

The locus of centres of given s1 , s2 is s1 – s2 =0

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