Ellipse general equation:
a * x ^ 2 + b * y ^ 2 + c * x * y + d * x + e * y + f = 0
You can use my package PlaneGeometry (soon on CRAN, hopefully):
library(PlaneGeometry)
ell <- EllipseFromEquation(A = 4, B = 2, C = 3, D = -2, E = 7, F = 1)
box <- ell$boundingbox()
plot(NULL, asp = 1, xlim = box$x, ylim = box$y, xlab = NA, ylab = NA)
draw(ell, col = "yellow", border = "blue", lwd = 2)