Science:Math Exam Resources/Courses/MATH105/April 2015/Question 01 (b)/Solution 1

Notice that $z$ must be a nonnegative number for any $x,y$. By setting $z$ to be some constant $k>0,$ we have

$k=x^{2}+y^{2}$

This equation represents circles of radius ${\sqrt {k}}$ (centered at the origin).

Therefore, the level curves of the paraboloid are $\color {blue}{\text{circles}}.$