SOLUTION: The length of the major axis of the ellipse below is 11, and the length of the red line segment is 4. How long is the blue line segment?

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