Ashwin and Harley are investigating the surface, $S,$ defined by

$p{x}^a+y+r{z}^b=E$

where the following conditions hold:

a and $b$ are either $1$ or $2,p$ and $r$ are non$-$zero real numbers and

$E$ is an integer.

Harley suggests looking at some cross sections of $S$ and makes the plots shown below.