How do you make a parametric plot of a table of functions in Mathematica?

Question

I am trying to generate a family of curves in a parametric plot (since the function is giving x as a function of y), but I am getting either nothing or clearly incorrect functions. Is there something special which you need to do to make a plot of such functions? This is my attempted code:

Clear[T, g, k, f, r, a, b, term]; T = 170 Degree;
f[s_, d_] = Normal[Series[Tan[T - ArcCos[-(d*s)]], {s, 0, 4}]]; 
r[h_, d_] = Simplify[Integrate[f[s, d], {s, 0, h}]];
a[h_] = Table[r[h, d], {d, 1, 3, 1}]
b[h_] = Table[-h, {Dimensions[a[h]][[1]]}];
ParametricPlot[{a[h], b[h]}, {h, 0, 100}, AspectRatio -> 1]

(Note: The y axis is inverted. I have tried here to make 2 lists with matching dimensions, to no effect. The easiest way to handle this was just to make the y parametric equation an inversion, since it is not easy to invert an axis in Mathematica)

Answer 1

You probably want this:

ParametricPlot[Transpose[{a[h], b[h]}], {h, 0, 100}, AspectRatio -> 1]