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I have a question: I have seen the formulas for focus/directrix of a parabola, but I cannot trust something unless I know how to get there.

How do I get the formulas of focus and directrix?

I got to an equation (X - Xf)^2 + (Y - Yf)^2 = (Y - Yd)^2 (distance between any point and focus equals to the distance between the same point and directrix). Where do I go from here?

Thank you!