Science:Math Exam Resources/Courses/MATH105/April 2011/Question 09 (e)/Statement

Each of the short-answer questions below is worth 5 points. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work.

In the box, write down which of the equations

$z=x^{2}+y^{2},\quad z=x^{2}-y^{2},\quad x^{2}+y^{2}+z^{2}=1,\quad z^{2}=x^{2}+y^{2}$

describes the surface with the following diagram?

If $z=f(x,y)$ is the equation of the surface in the diagram, sketch in the space provided below the level curve of $f$ at height $z=2.$ Provided explicit labels for your sketch.