I'm having trouble with the following problem: "Consider the parabolic mirror given by the equation $z=x^2+y^2$. Show that when the rays of light that travel paralell to the $z$ axis pass through the same point when reflected." I'm familiar with the law of reflection but I'm stuck because I don't know how to apply vector calculus to this situation. I have tried to apply the law of reflection but I can't seem to get anywhere. Thanks.