Answer
The answer is below.
Work Step by Step
From the isotherm curves are the level curves of the given function $T(x, y)=x y,$ at $T=1$, we have:
\[
1=x y \Rightarrow 1 / x=y
\]
At $2=T$, the result is:
\[
2=x y \Rightarrow 2 / x=y
\]
and at $3=T$
\[
3=x y \Rightarrow 3 / x=y
\]
If the ant wants to walk on the plate and the temperature along the path remains constant, the ant moves along a isotermal curve. Since the ant is initially at $P(1,4),$ the result is
\[
k=x y \text { where } k=1(4) \Rightarrow 4=k
\]
So, the ant moves along the isoterm
\[
4 / x=y \quad \text { or } \quad 4=x y
\]
