par( mai = c(0.5,0.5,0.1,0.1) )
plot(c(-5,10),c(-5,10),type="n",xlab="", ylab="", asp=1)
abline(h=-6:16, v=-6:16, lty=2, col="grey50")
abline(h=seq(-6,16,1/2), v=seq(-6,16,1/2), lty=3, col="grey50")
abline(v=0,h=0,col="blue")
t <- seq(0,2*pi,len=1000)
a1 <- 4.5+runif(1)*3; a2 <- 2.5+runif(1)*2; x <- a1*cos(t); y <- a2*sin(t)
t1 <- c(0,pi); x1 <- a1*cos(t1); y1 <- a2*sin(t1)
t2 <- c(pi/2,pi*3/2); x2 <- a1*cos(t2); y2 <- a2*sin(t2)
ang <- runif(1)*2*pi; dx <- 2.5; dy <- 2.5
X1 <- x1*cos(ang)-y1*sin(ang)+dx; Y1 <- x1*sin(ang)+y1*cos(ang)+dy
X2 <- x2*cos(ang)-y2*sin(ang)+dx; Y2 <- x2*sin(ang)+y2*cos(ang)+dy
X <- x*cos(ang)-y*sin(ang)+dx; Y <- x*sin(ang)+y*cos(ang)+dy
lines(X,Y); lines(X1,Y1); lines(X2,Y2)
# trova l'area dell'elisse ragionando solo sul grafico e controllala
# battendo  pi*a1*a2