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Show that the centers of the family of circles passing through a point is a parabola

by RoRi

Prove that the set of the centers of the family of circles all of which pass through a given point and are tangent to a given line forms a parabola.

Proof. Incomplete.

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):