Mathematics

Problem

The ellipse

E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1

is inscribed in a rectangle

R

whose sides are parallel to the coordinate axes. Another ellipse

E_2

passing through the point

(0, 4)

circumscribes the rectangle

R

. The eccentricity of the ellipse

E_2

is a.

\frac{\sqrt{2}}{2}

\frac{\sqrt{3}}{2}

\frac{1}{2}

\frac{3}{4}