Simulation of ellipse axis

问题

I've like to simulate ellipse axis, in my example:

a <- x # semi-major axis 
e <- 1/sqrt(2) # eccentricity 
b <- a * sqrt(1 - e^2) # semi-minor axis
c  <- 6.3 # ellipse area

My code needs to estimate with 999 replicates a mean major axis (a) when I have the mean eccentricity (e) and differents minor axis (b) and ellipse areas (c). Any idea? Thanks

回答1:

a = x 
b = x * sqrt(1 - e^2)

area = pi * x * x * sqrt(1 - e^2) = pi * x^2 * sqrt(1 - e^2)

x = sqrt( area / (pi * sqrt(1 - e^2)) );

来源：https://stackoverflow.com/questions/55675591/simulation-of-ellipse-axis