Plot-Befehle in Mathematica am Beispiel der Ellipse

Plot der Kurve in Parameterform

a = 3; b = 2;

c[t_] := {a Cos[t], b Sin[t]}

ParametricPlot[
      c[t], {t, -π, π}, 
AspectRatio -> 
        Automatic, 
      Axes -> 
        False, 
Epilog -> {Line[{{-a, 0}, {a, 
                0}}], Line[{{0, -b}, {0, b}}]}]

Plot der Kurve in Polarkoordinaten

e := Sqrt[a^2 - b^2]
ϵ := e/a
r[ϕ_] := 1/(1 + ϵ Cos[ϕ])

<< Graphics`Graphics`

PolarPlot[r[ϕ], {ϕ, -π, π}, 
      AspectRatio -> Automatic, Ticks -> False]

Plot der implizit gegebenen Kurve

<< Graphics`ImplicitPlot`

F[x_, y_] := (x/a)^2 + (y/b)^2

ImplicitPlot[ F[x, y] == 1, {x, -a, a}, {y, -b, b}, 
      Axes -> False, AspectRatio -> Automatic, 
      Epilog -> {Line[{{-a, 0}, {a, 0}}], 
          Line[{{0, -b}, {0, b}}]}]

Plot der explizit gegeben Kurve

Clear[a, b]

sol = Solve[F[x, y] == 1, {y}]

f1 = Function[x, y /. sol[[1]]]
f2 = Function[x, y /. sol[[2]]]

f1[x]

a = 3; b = 2;
Plot[f1[x], {x, -a, a}, AspectRatio -> Automatic, 
      Ticks -> None]

Plot[{f1[x], f2[x]}, {x, -a, a}, AspectRatio -> Automatic, 
      Ticks -> None]