In the Cartesian coordinate plane, an ellipse with center at the origin and foci at points E and F is given below. The vertical line drawn from point F intersects the ellipse at points, and the point with positive y-coordinate is denoted by K. The equation of the line passing through points K and E is $\mathrm { y } = \mathrm { x } + 1$.
Accordingly, what is the value of a?
A) $\sqrt { 2 } + 1$
B) $\sqrt { 3 } + 2$
C) $\sqrt { 5 } + 1$
D) $3 - \sqrt { 2 }$