(v_x, v_y) (assuming focus (f_x, f_y))

(drawn with rotation angle 0°)

semi-axis length | sqrt((f_x - v_x)^2 + (f_y - v_y)^2) focal parameter | 2 sqrt((f_x - v_x)^2 + (f_y - v_y)^2) eccentricity | 1 directrix | y = -f_x^2/(f_y - v_y) - (x f_x)/(f_y - v_y) + (3 f_x v_x)/(f_y - v_y) - (2 v_x^2)/(f_y - v_y) + (x v_x)/(f_y - v_y) - f_y + 2 v_y (assuming focus (f_x, f_y) and vertex (v_x, v_y))