Answer
No, each of these portions can not be a parabola.
Work Step by Step
No, each of these portions can not be a parabola.
The equation of a parabola has this form:
$y = ax^2+bx+c$
A parabola is the graph of a continuous function that only increases to $\infty$ (or $- \infty$) as $x$ goes to $\infty$ or $-\infty$. However, each portion of $y = sec~x$ or $y = csc~x$ approaches $\infty$ even though the value of $x$ is limited by an asymptote.
Therefore, each of these portions of $y = sec~x$ or $y = csc~x$ can not be a parabola.