There is no relation. In fact, they're more alike than different
This is probably not what you or your teacher wants, but they have nothing to compare.
Conservation of Energy just means that energy is not lost but is only turned into something else.
Entropy increase just means that all the particles in the universe is getting more random since the universe is expanding and there are more places to fill.
The only way I see these two relate is that the energy dissipates into the universe due to entropy increase. But it doesn't disappear or anything.