Setting sqrt(1-a^2/3) = 2- a

we get a = 3/2 this is the point where the point distance from(a,0) to a point on the ellipse is the same as the distance from (a,0) to the vertex(2,0)

In fact for a = sqrt(3) sqrt(1-a^2/3) = 0 and sqrt(1-a^2/3) is imaginary

for a > sqrt(3)

If you want I made an animation demonstrating this on my web site:

Scratch Paper