As I don't want you to expend all your energy
on the intricacies of maple here are commands that
you can use for the plots of Q5.5 (and 5.10).

If you have time try changing the ranges for t in (b) and
(c) to see what happens and why there have to be 3 plots.

>with(plots):

5.5(a)

> plot([t/(1+t^4),t^2/(1+t^4),t=-1000..infinity],x=-1..1,-1..1,thickness=5,
scaling=constrained,numpoints=1000,xtickmarks=3,ytickmarks=3,
axesfont=[TIMES,ROMAN,18]);

(b) combine the 3 following on one plot using display

> plot([t/(1-t^4),(t^2)/(1-t^4),t=1.2..100],x=-1..1,-1..1,thickness=5,
scaling=constrained,numpoints=1000,xtickmarks=3,ytickmarks=3,
axesfont=[TIMES,ROMAN,18]);
> plot([t/(1-t^4),(t^2)/(1-t^4),t=-0.9999..0.9999],x=-1..1,-1..1,
thickness=5,scaling=constrained,numpoints=1000,xtickmarks=3,
ytickmarks=3,axesfont=[TIMES,ROMAN,18]);
> plot([t/(1-t^4),(t^2)/(1-t^4),t=-100..-1.2],x=-1..1,-1..1,thickness=5,
scaling=constrained,numpoints=1000,xtickmarks=3,ytickmarks=3,
axesfont=[TIMES,ROMAN,18]);

> plot([(2*t^2-1)/(1+t^3),t*(2*t^2-1)/(1+t^3),t=-0.99..100],x=-3..3,-3..3,
thickness=5,scaling=constrained,numpoints=10000,xtickmarks=3,
ytickmarks=3,axesfont=[TIMES,ROMAN,18]);
> plot([(2*t^2-1)/(1+t^3),t*(2*t^2-1)/(1+t^3),t=-1000..-1.1],x=-3..3,-3..3,
thickness=5,scaling=constrained,numpoints=1000,xtickmarks=3,
ytickmarks=[-3,0,3],axesfont=[TIMES,ROMAN,18]);

(d)

> plot([-(1+t^3)/(1+t^4),t*(1+t^3)/(1+t^4),t=-10000..infinity],
x=-1.5..1,-1..1.5,thickness=5,scaling=constrained,numpoints=1000,
xtickmarks=3,ytickmarks=3,axesfont=[TIMES,ROMAN,18]);