the length of the major axis of the ellipse below is 13 what is the sun of the lengths of the red and blue line segments

The distances a, b, and c, in an ellipse, are related like this
[tex]a^2=b^2+c^2[/tex]Where 2c is 13, according to the problem.
Let's find c
[tex]\begin{gathered} 2c=13 \\ c=\frac{13}{2}=6.5 \end{gathered}[/tex]The blue line is equal to a, and the sum of the red and blue lines is 2a.