plotting – Plot ellipses in a exponential curve


I am trying to produce a single plot, where the ellipses fits neatly within the given curve function, and with each intersecting the curve at exactly 4 points.

  • The ellipses is $x^2/a^2+y^2/b^2=1$, where $a=0.5, 0.6, 0.7, …,
    2.0$
    , where $a>0$,$b>0$ and $πab=5$. Hint: use Table to create all of them in one command.

  • The curve $|y|=5/(2π|x|)$, drawn in black. Be sure that the curve
    appears, and draw the single curve on top of the ellipses so that it
    is clearly visible.

What I tried to do was

Clear(x, y)
ellipse = x^2/a^2 + y^2/b^2 == 1;
curve = Abs(y) == 5/(2*Pi*Abs(x));
ell = Table(ellipse, {a, 0.5, 2.0, 0.5}, {b, 5/Pi*a});
curvep = ContourPlot(Evaluate(curve), {x, -7, 7}, {y, -7, 7}, 
   ContourStyle -> Black);
ellipsep = 
  ContourPlot(Evaluate(ell), {x, -7, 7}, {y, -7, 7}, 
   ContourStyle -> Rainbow);
Show(ellipsep, curvep)

but for some reason, my ellipses are not fitting inside the curve function and rather it is outside.

enter image description here