if 6 and 12 are the lengths of the segments of any focal chord of a parabola, then the length of semi-latus rectum i

The question seems to be incomplete. However, if you're asking for the length of the semi-latus rectum of a parabola given the lengths of the segments of any focal chord, here's how you can calculate it:

The property of a parabola is that the product of the lengths of the segments of any focal chord is equal to the square of the semi-latus rectum.

Let's denote the lengths of the segments of the focal chord as p and q, and the semi-latus rectum as l. Then, according to the property, we have:

p*q = l^2

In your case, p = 6 and q = 12. Substituting these values into the equation, we get:

6*12 = l^2 72 = l^2

Taking the square root of both sides, we find:

l = sqrt(72) = 8.49 (approximately)

So, the length of the semi-latus rectum is approximately 8.49.