Fill Specific Area Inside an Ellipse in R

Question

I'm trying to create a plot in R using ggplot2 and ggforce that contains an ellipse. Inside this ellipse, I want to fill a specific area the area (e.g., where x>0 and y>0) with blue color.

Here's some code that draws the ellipse but doesn't but without the filling:

library(ggplot2)
library(ggforce)

# Generate ellipse data for ggforce
ellipse_data <- data.frame(
    x0 = 0,
    y0 = 0,
    a = 2,
    b = 3,
    angle = 0
)

ggplot() +
    geom_ellipse(data = ellipse_data, 
                 aes(x0 = x0, y0 = y0, a = a, b = b, angle = angle), 
                 fill = NA, color = "black") +
    coord_fixed() +
    xlim(-3, 3) +
    ylim(-3, 3)

This is what I expect:

The solution should work for any ellipse and other specific areas, e.g., x > 1 and y > 0.5