Getting the ellipse function to match the dataEllipse function in R

Question

So I am sampling from a multivariate normal distribution in R, and am trying to figure out how to calculate its 95% confidence ellipse using the ellipse() function in the package car.

Here is some code I am running:

mu = c(0,0)
sigma = matrix(c(20,0,0,45),nrow=2)

z = rmvnorm(10000,mu,sqrt(sigma))

par(mfrow=c(1,2))
plot(z)
ellipse(mu,sqrt(sigma*qchisq(.05,2)),radius=1)
dataEllipse(z,levels=.95)

So basically I want the ellipse command to replicate the dataEllipse command. If anyone has any suggestions that would be greatly appreciated!

Edit: Using Dwins code and combining it within my own:

library(car)
library(mvtnorm)

mu = c(0,0)
sigma = matrix(c(20,0,0,45),nrow=2)

z = rmvnorm(10000,mu,sqrt(sigma))

dataEllipse(z,levels=.95)
car::ellipse(mu, sigma*qchisq(.05,2), col="blue", 
                 radius=sqrt(2 * qf(.975, 2, 9998)) )

So as you can see, the ellipses are still not the same...

Answer 1

Since this post is still getting views, I'll provide the actual answer. The last three lines of this code snippet replicates car::dataEllipse exactly:

library(car)
library(mvtnorm)

mu = c(0,0)
sigma = matrix(c(20,0,0,45),nrow=2)
z = rmvnorm(10000,mu,sigma)

dataEllipse(z,levels=.95)

center <- apply(z, 2, mean)
cov_mat <- cov(z)
ellipse(center, cov_mat, col="red", radius=sqrt(2 * qf(.95, 2, 9999)))

Note that both car::dataEllipse and car::ellipse return the coordinates of the points silently, so one can confirm that the points are indeed equal.