KöMaL 2023 B5317

An ellipse lies in the closed positive orthant, its foci are $(x_1;y_1)$ and $(x_2;y_2)$, and it touches the coordinate axes at the points of abscissa $p$, and ordinate $q$, respectively. Show that the point $(p;q)$ is collinear with the origin and the centre of the ellipse, and calculate the numerical eccentricity of the ellipse.