The temperature at any point in the plane is given by $\displaystyle T(x,y) = \frac{120}{x^{2}+y^{2}+3}$.

(a) What shape are the level curves of $T$?
A. lines
B. ellipses
C. hyperbolas
D. circles
E. parabolas
F. none of the above

(b) At what point on the plane is it hottest?
What is the maximum temperature?

(c) Find the direction of the greatest increase in temperature at the point $(2,3)$.
What is the value of this maximum rate of change, that is, the maximum value of the directional derivative at $(2,3)$?

(d) Find the direction of the greatest decrease in temperature at the point $(2,3)$.
What is the value of this most negative rate of change, that is, the minimum value of the directional derivative at $(2,3)$?