If $(u,v)$ is a point on $4x^2+a^2y^2=4a^2$,where $4<a^2<8$,that is farthest from $(0,-2)$ then $u+v$ is equal to?

My Approach:

I took a parametric point $(t,4-4t^2/a^2)$.And then tried to find the minima of the distance.But that is too lengthy method.Any other suggestions?