Calculate the eccentricity of ellipses

Question

I've like to calculate the eccentricity of ellipses x, in my example:

#Artificial ellipse
a <- 1 # semi-major axis 
e <- x# eccentricity 
b <- a * sqrt(1 - e^2) # semi-minor axis
c <- 1.3 # ellipse area

But I need to make this using the ellipse area (c) in the calculation. This is poisible?

Answer 1

b = c/(pi*a);
x = (sqrt(a^2 - b^2))/a;

is the formula you need. Or put togther:

x = (sqrt(a^2 - (c/(pi*a))^2))/a;