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Analytic geometric parabola?
As shown in the figure, the points of p, n, H N and h on the abscissa are P', N' and H' respectively. The ratio of the length of the line segment OH and ON in the title is actually the ratio of the abscissa of H and N (similar to a triangle).

The coordinate of question M is (0, t), so the coordinate of point P is (t? /2p, t) The coordinate of n point is (t? /p,t)

Therefore, the equation of the straight line above is: y=(p/t)x, and the coordinate of point H can be obtained by combining with the parabolic equation as (2t? /p,2t)

So | Oh |/| On |=2