Relation of Virgo to the North Star?

Answer 1

Essentially none. Polaris, the north star, is positioned almost (but not quite) exactly above the north pole of the Earth. This is entirely coincidental, as the precession of the Earth's rotation causes the Earth to wobble in a 26,000 year cycle. Polaris wasn't the north star 3000 years ago, and in 3000 years, it won't be then - but it is now.

Virgo, one of the zodiacal constellations, is more or less level with the ecliptic.

Answer 2

Virgo is a zodiac constellation in the southern celestial hemisphere, while the North Star (Polaris) is located near the celestial north pole. As such, Virgo and the North Star are not directly related, as they are found in different regions of the sky.