Conics Sections: proof that M belongs to a fixed conic of directrix (D)

[Ali Ali]

Given two distinct point A and B, and consider an arc of variable circle of extremeties A and B, on this arc the point M and M' such that meas AM ( arc)= meas MM' = meas M'B. Let (D) be the perpendicular bisector of AB and I midpoint of [MM'] .
proof that M belongs to a fixed conic of directrix (D)

 

[Deleted member 4993]

Given two distinct point A and B, and consider an arc of variable circle of extremeties A and B, on this arc the point M and M' such that meas AM ( arc)= meas MM' = meas M'B. Let (D) be the perpendicular bisector of AB and I midpoint of [MM'] .
proof that M belongs to a fixed conic of directrix (D)

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[Ali Ali]

okay thank for your reply

proving that MA > MI surely will prove it as a hyperbola which I think is the solution