Given the parabola , the point on the focal chord is . We need to determine how the focus divides the chord.

First, express the coordinates for the point using the parametric form of the parabola.
The general parametric equations for the parabola are:

The equation leads to solving for :

Now, find the coordinates of point using the relation . Therefore:

Given the focus of the parabola is at , we can find the lengths of and :

The length is calculated as:

And is given by:

Since the focus divides the chord in a specific ratio , and , we find:

Thus, the squares of and sum up to:

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