plot - How to draw a small bivariate distribution in R?

Question

For illustrative purposes, I am trying to draw a small bivariate normal distribution. I would like it to be tight, centered at (3,4;1), and with a radius of 0.5 or less. By that, I mean that I would like the datapoints to be confined within a small radius.

Below see the code I am using (from this website); I have tried to tweak it in different ways, but the bivariate is always spread out.

library(MASS)
N <- 200 # Number of random samples
set.seed(123)
# Parameters 
rho <- 0.5
mu1 <- 3.4; s1 <- 1
mu2 <- 1; s2 <- 1

# Parameters for bivariate normal distribution
mu <- c(mu1,mu2) # Mean 
sigma <- matrix(c(s1^2, s1*s2*rho, s1*s2*rho, s2^2),
                2) # Covariance matrix
X <- mvrnorm(N, mu = mu, Sigma = sigma)
z <- kde2d(X[,1], X[,2], n=50)

plot(X, xlab="X label", ylab="Y label", 
    xlim=c(2,6), ylim=c(-1,3.5),pch=19, cex=.4)
contour(z, drawlabels=FALSE, add=TRUE)

^{Created on 2021-01-05 by the reprex package (v0.3.0)}

Answer 1

Using s2 <- s1 <- 0.25 solves the problem as pointed out by @user20650.

library(MASS)
N <- 200 # Number of random samples
set.seed(123)
# Parameters 
rho <- 0.5
mu1 <- 3.4; s1 <- 0.25
mu2 <- 1; s2 <- 0.25

# Parameters for bivariate normal distribution
mu <- c(mu1,mu2) # Mean 
sigma <- matrix(c(s1^2, s1*s2*rho, s1*s2*rho, s2^2),
                2) # Covariance matrix
X <- mvrnorm(N, mu = mu, Sigma = sigma)
z <- kde2d(X[,1], X[,2], n=50)

plot(X, xlab="X label", ylab="Y label", 
    xlim=c(2,6), ylim=c(-1,3.5),pch=19, cex=.4)
contour(z, drawlabels=FALSE, add=TRUE)

^{Created on 2021-01-05 by the reprex package (v0.3.0)}