Prove that the intersection between a quadric and a plane is always a second-order curve

Question

My problem is simply: If you have a general quadratic surface $$ Q: ax^2+by^2+cz^2+2fyz+2gzx+2hxy+2px+2qy+2rz+d=0.$$ prove that the intersection curve between this suface and a plane $$ P: a_1 x + a_2 y + a_3 z + a_4 = 0.$$ is always a second-order curve (a conic section or two parallel lines).