C'C" : B'B" = constant;
whence
The segments cut off on any two tangents to a parabola by a variable tangent are proportional.
If now we take the tangent B'C' as axis of ordinates, and the diameter through the point of contact O as axis of abscissas, calling the coordinates of B(x, y) and of C(x', y'), then, from the similar triangles BMD' and we have
y : y' = BD' : D'C = BB' : AB'.
Also
y : y' = B'D' : C'C = AC' : C'C.
If now a line is drawn through A parallel to a diameter, meeting the axis of ordinates in K, we have
AK : OQ' = AC' : CC' = y : y',
and