The line FL perpendicular to the axis, G D and passing through the focus, is the semilatus rectum, the latus rectum being the focal chord parallel to the directrix.
This is a parabola with vertical axis, of latus-rectum 2uiulg.
Now in a conic whose focus is at 0 we have where 1 is half the latus-rectum, a is half the major axis, and the upper or lower sign is to be taken according as the conic is an ellipse or hyperbola.
This is recognized as the polar equation of a conic referred to the focus, the half latus-rectum being hf/u.
Then the square of the ordinate intercepted between the diameter and the curve is equal to the rectangle contained by the portion of the diameter between the first vertex and the foot of the ordinate, and the segment of the ordinate intercepted between the diameter and the line joining the extremity of the latus rectum to the second vertex.