Given that b and c are lengths of the segments of any focal chord of the parabola y² = 4ax.

We know that the length of the latus - rectum is 4a.

We know that the semi - length of the latus - rectum is the harmonic mean of any length of any focal chord.

We know that if a, b, c are in harmonic progression, harmonic mean is given by,

⇒

Here the length of semi-latus rectum is 2a.

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⇒

⇒

Length of the latus - rectum is 4a,

⇒

∴The length of the latus - rectum is .