Draw a parabola as the graph of a function y = p*x2. p (positive) relates to the parameter k of the parabola which is the distance (|FL| below) of the focus to the directrix. It is k = 1/(2*p).
To prove it, find B on the graph at x=1, f(1) = p. Draw the tangent (DB) at B and take the symmetric of line AB with respect to this tangent. This is line BE' intersecting the y-axis on the focus of the parabola. The tangent at B and the parallel to it from D form a rhombus ABFD, whose diagonals intersect orthogonally at K(x = 1/2). Then (KE)2 = p*|EA| ==> |EA| = |FC| = 1/(4*p). The parameter being given by |FL| = 2*|FC| = 1/(2*p).
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Parabola parameter ![[0_0]](ParabolaParameter_files/ParabolaParameter_0_0_0.png)
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