I'm trying to read your mind.  

I will guess that the red line is the semi-minor-axis, b.

I will guess that the blue line you want to find connects the top
(co-vertex) to a focal point (or focus).  

The semi-major axis is  of the major axis, a, so a = .




First we find c, which is the distance from the center to the focus.

All elipses have the property

c² = a² - b²

c² =  - 4²

c² =  - 16

c² =  - 

c² = 

By the Pythagorean theorem,


(blue line)² = c² + b²

(blue line)² =  + 4²

(blue line)² =  + 

(blue line)² =  + 

(blue line)² = 

(blue line)² = 

blue line = 

blue line = 

So the blue line is equal to the semi-major axis.

Edwin