Stop there, locus!

Geometry Level 3

Find the equation of the locus of a point which moves such that the ratio of its distances from \((2,0)\) and \((1,3)\) is \(5:4\).

If the equation can be written as \(9{ x }^{ 2 }+{ 9y }^{ 2 }+14x-150y+\alpha =0\), find \(\alpha\).

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