I'm not a physics major student and I call myself a total noob in physics, however, I have this issue to solve. The problem is that I don't even know where to start from. One little thing to add: this problem was translated from another language so forgive me for some misunderstandings. I'm not asking for a full solution(even though it would be highly appreciated), I need more like a guide where to dig.
A point particle of mass m moves under the force of gravity on the surface of a paraboloid.
$z = x^2 + y^2$
Write the equations of motion.