What constellation is the earth in?
It depends where you are looking from. From our nearest neighbouring star (not counting the Sun) we would be in Cassiopeia.
Constellations are relative to the observer.
From the Alpha Centauri system (3 stars including Proxima Centauri a.k.a. Alpha Centauri C) our sun would appear as an extra star in the constellation of Cassiopeia.
From Barnard's star our sun would appear as a bright extra star in the constellation of Monoceros.