Is it possible to plot a two-set/disc Venn diagram with proportional discs and intersection without having to use the below "trial-and-error" code? In the example below the left disc has 6 elements (disc area = 6), the right disc has 4 elements (disc area = 4) and the intersection has 2 elements (area = 2)
a1 = 6;
a2 = 4;
a1capa2 = 2;
d = 1.21;
y1[x_] := Sqrt[a1/π - x^2]
y2[x_] := Sqrt[a2/π - (x - d)^2]
Plot[
{y1[x], -y1[x], y2[x], -y2[x]}, {x, -2, 4},
AspectRatio -> Automatic, PlotStyle -> {Black}
]
x0 = x /. Solve[y1[x] == y2[x], x][[1]]
caparea = 2 (N[Integrate[y2[x], {x, d - Sqrt[a2/π], x0}]] +
N[Integrate[y1[x], {x, x0, Sqrt[a1/π]}]]
)
Here I have to guess the distance $d$ between the discs in order to get the intersection area, caparea, to the requested 2. (It also give an imaginary reply, which I find odd.)
I'm looking for a solution where you only input the disc areas, and the intersection area and the distance $d$ is calculated and the graph plotted.
There are several other solutions for Venn diagrams but they all seem to have the same disc size.
TIA.