Let (x,y) be any arbitrary point on the ellipse.
distance of (x,y) from (0,4), d₁=
distance of (x,y) from the line y-9=0, d₂ =
(Note that distance of a point (X,Y) from a line ax+by+c=0 is
given that d₁ = 2/3 d₂
This is the required equation of the ellipse.