# 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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