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The chord lengths obtained by the section line of moving circle 3x-y = 0 and 3x + y = 0 are 8 and 4 respectively
As shown in the figure, let point m (x, y) be obtained from the condition, ab = 4, EC = 2, from the distance formula from point to straight line, ma2 = (3x − y) 210, MC2 = (3x + y) 210, from the vertical diameter theorem, ma2 + AB2 = MC2 + EC2, and (3x − y) 210 + 16 = (3x + y) 210 + 4, from simplification, xy = 10. The trajectory equation of point m is xy = 10
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