Can we find the two circles that satisfy these three conditions?

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Find the equations of the two circles which each satisfy the following conditions:

1. the axis of \(x\) is a tangent to the circle,

2. the centre of the circle lies on the line \(2y = x\),

3. the point \((14,2)\) lies on the circle.

Prove that the line \(3y = 4x\) is a common tangent to these circles.