Are you good at finding locus

Geometry Level 5

The base of a triangle passes through a fixed point \(P(a,b)\) and it's side's are bisected at right angle by the pair of straight line \(y^{2}-8xy-9x^{2}\) . The locus of its vertex is \(ω(x^{2}+y^{2})+(4a+5b)x+4b-5a=0\). Find \(ω\).

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