Distance between directrices: \(d =8 =\frac{2a}{e}\)

Distance between foci: \(2c = 2 = ea\)

\(e = \frac{a}{4}\)

\(e = \frac{1}{a}\)

\(a = 2\)

Center at the origin and major axis parallel to x-axis: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

\(b^2 = a^2 - c^2\)

\(b^2 = 4 - 1 = 3 \)

\(\frac{x^2}{4} + \frac{y^2}{3} = 1\). Answer

\(3x^2 +4y^2 = 12\). Simplified Answer