# 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.