Casting AoE spells while mounted

If I'm riding a mount and I cast Burning Hands (15 foot cone), does my mount take damage? What about something emanating from me, like Arms of Hadar?

Quote from karakune>>

If I'm riding a mount and I cast Burning Hands (15 foot cone), does my mount take damage?

 I guess this depends on how you angle it, but it could take damage, yes.

EDIT: as a DM, I'd rule if you point the cone straight forward, your mount is safe.

What about something emanating from me, like Arms of Hadar?

 I think so, because your mount is a creature.

Invoking Hadar, you cause tendrils to erupt from yourself. Each creature in a 10-foot Emanation originating from you makes a Strength saving throw.